section 9.6

1. Fill in each blank so that the resulting statement is true. A conic section is the set of all points in the plane such that the ratio of the distance from a fixed point, called the , to the distance from a fixed line, called the _ , equals a constant e, called the If e = 1 the conic is a(n). If e 1, the conic is a(n) A conic section is the set of all points in the plane such that the ratio of the distance from a fixed point, called the (1) to the distance from a fixed line, called the (2) equals a constant e, called the (3) If e = 1 the conic is a(n) (4) . If e 1, the conic is a(n) (6) (1) O directrix, (2) O directrix, (3) O directrix. (4) O parabola. (5) O parabola. eccentricity, focus, O eccentricity. O hyperbola. O ellipse. focus, O eccentricity, focus. ellipse. O hyperbola. (6) O parabola. O hyperbola. O ellipse. 2. Fill in each blank so that the resulting statement is true. For all four equations shown below, the focus is at the and e represents the conic's Click here to view the standard forms of the polar equations of conics. For all four equations shown below, the focus is at the (1) and e represents the conic's (2) 1: Standard Forms of the Polar Equations of Conics ep re- Directrix is perpendicular to the polar axis at a distance p units to the right of the pole. 1 + e cos 0 ep b. T=. Directrix is perpendicular to the polar axis at a distance p units to the left of the pole. 1 - e cos 0 ep C. T= Directrix is parallel to the polar axis at a distance p units above the pole. 1 +e sin 0 ep d. T= Directrix is parallel to the polar axis at a distance p units below the pole. 1 -e sin 0 (1) O pole (2) O directrix. O eccentricity O eccentricity. origin O pole. directrix O origin.3. Fill in each blank so that the resulting statement is true. 18 Consider the equation r= 1+ 18 cos 0 . = _ so this is the equation of a(n) . P= so the directrix is to the polar axis at a distance of _ _ unit(s) to the of the pole. 2 Click here to view the standard forms of the polar equations of conics. 18 Consider the equation r= 1+ 18 cos p. = so this is the equation of a(n) (1) so the directrix is (2) to the polar axis at a distance of unit(s) to the (3) of the pole. (Type whole numbers.) 2: Standard Forms of the Polar Equations of Conics ep a. Directrix is perpendicular to the polar axis at a distance p units to the right of the pole. 1 +e cos 0 ep b. re. Directrix is perpendicular to the polar axis at a distance p units to the left of the pole. 1 -e cos 0 ep C. re- Directrix is parallel to the polar axis at a distance p units above the pole. 1 + e sin 0 ep d. r=- Directrix is parallel to the polar axis at a distance p units below the pole. 1 -e sin 0 (1) O parabola. (2) O parallel (3) O left O ellipse. O perpendicular O right O hyperbola.4. Fill in each blank so that the resulting statement is true. 18 Consider the equation r= 1 - sing.es _ so this is the equation of a(n) so the directrix is to the polar axis at a distance of unit(s) to the of the pole. Click here to view the standard forms of the polar equations of conics. 18 Consider the equation r = 1 - sing" so this is the equation of a(n) (1). so the directrix is (2) to the polar axis at a distance of unit(s) (3) the pole. (Type whole numbers.) 3: Standard Forms of the Polar Equations of Conics ep a. r= - Directrix is perpendicular to the polar axis at a distance p units to the right of the pole. 1 + e cos 0 ep b. re- Directrix is perpendicular to the polar axis at a distance p units to the left of the pole. 1-e cos 0 ep C. 1 +e sin 9 Directrix is parallel to the polar axis at a distance p units above the pole. ep d. 1 -e sin 0 Directrix is parallel to the polar axis at a distance p units below the pole. (1) O hyperbola. (2) O parallel (3) O below O parabola. O perpendicular O above O ellipse.5. Fill in each blank so that the resulting statement is true. 16 The equation r= 2-2 cos 0 is not in standard form because the constant term in the denominator is not _ _. The equation can be written in standard form by 16 The equation r=- 2-2cos 0 is not in standard form because the constant term in the denominator is not . The equation can be written in standard form by (1) (Type whole numbers.) (1) O dividing the numerator by O dividing the numerator and denominator by O dividing the denominator by a. Identify the conic section that the polar equation represents. b. Give the location of the directrix from the focus located at the pole. 8 1 + sin 0 a. Identify the conic that our polar equation represents. O Parabola O Hyperbola O Ellipse b. Is the directrix perpendicular to the polar axis or parallel to the polar axis? O Perpendicular O Parallel Which direction is the directrix from the pole? O Left O Above Below Right How far is the directrix from the pole? units (Type an integer or a simplified fraction.)I". 5. Identify the conic section that the polar equation represents. h. Give the location of the dlrectm: from the focus located at the ode. 2 r=.=.+iisin n 3. Identify the conic that our polar equation represents. in) Parabcla if} Hyperbola CI Ellipse b. Is the direcuix perpendicular to the polar axis or parallel to the polar axis? 0 Perpendicular 0 Parallel Which direction is the directrix from the pole? Cl Below fJ Above '1') Left C) Flight -low far is the directrix from the pale? units [Type an integer or a simplied fraction.) E. {at Identify the conic section that the polar equation represents. {in} Describe the location of the directrix om the focus located all the pole. _ 8 r 2+2cos' {at What type of conic section does the polar equation represent? If) Hyperbola t\") Ellipse \"I\"?! Parabola {in} Describe lhe location of the dilectrix om the focus located all the pole. C) The directrix is 4 units above the pole, at y = at. L\") The direch'iit is 4 units to the right of the pole. at x = 4. O The directrlx led units to the Ian of the pole. al is = d. t") The directrix is 4 units below the pole. at 5; = -4. 9. a. Identify the conic section that the polar equation represents. b. Give the location of the directrix from the focus located at the pole. 5 6+9sin 0 a. Identify the conic that our polar equation represents. O Hyperbola O Parabola O Ellipse b. Is the directrix perpendicular to the polar axis or parallel to the polar axis? O Perpendicular O Parallel Which direction is the directrix from the pole? O Below O Above O Left O Right How far is the directrix from the pole? units (Type an integer or a simplified fraction.)10. Graph the polar equation. O A. OB. 7 r= - 1+ sind Write the equation in one of the standard forms. Identify the value of e. O C. OD. e= Identify the value of p. P = Identify the conic. Choose the correct answer below. OE. OF. O Parabola O Hyperbola O Ellipse Identify the directrix. (Type an equation.) Identify the vertex(vertices). (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) Which of the following graphs to the right is the correct graph of the equation?11. Graph the polar equation. O A. O B. 5 r= 1 - cos 0 Write the equation in one of the standard forms. r= Identify the value of e. O c. OD. Identify the value of p. P= Identify the conic. Choose the correct answer below. OE. OF. O Hyperbola O Parabola O Ellipse Identify the directrix. (Type an equation.) Identify the vertex(vertices). (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) Which of the following graphs to the right is the correct graph of the equation?12. Graph the polar equation. O A. OB. 21 r= 3-3 cos 0 Write the equation in one of the standard forms. r= Identify the value of e. O c. OD. Identify the value of p. P Identify the conic. Choose the correct answer below. OE. OF. Hyperbola O Parabola 10 O Ellipse Identify the directrix. (Type an equation.) Identify the vertex(vertices). (Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to separate answers as needed.) Which of the following graphs to the right is the correct graph of the equation?13. Graph the polar equation. O A. OB. 20 r= 2+ 10 cos 0 Write the equation in one of the standard forms. THE r= Identify the value of e. O c. OD. e = 0 Identify the value of p. P = Identify the conic. Choose the correct answer below. OE. OF. Parabola O Ellipse O Hyperbola Identify the directrix. (Type an equation.) Identify the vertex(vertices). Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type an exact answer, using it as needed.) Which of the following graphs to the right is the correct graph of the14. Graph the polar equation. O A. OB. 8 2-4 cos 0 Write the equation in one of the standard forms. Identify the value of e. O c. OD. e= Identify the value of p. P = Identify the conic. Choose the correct answer below. O E. F. O Hyperbola O Parabola O Ellipse Identify the directrix. (Type an equation.) Identify the vertex(vertices). Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type an exact answer, using a as needed.) Which of the following graphs to the right is the correct graph of the equation? 15. Fill in each blank so that the resulting statement is true. 15 The equation r= `5-5 cose Is not in standard form because the constant term in the denominator is not _. The equation can be written in standard form by 15 The equation = 5-5 cos 0 is not in standard form because the constant term in the denominator is not . The equation can be written in standard form by (1) "Type whole numbers. (1) O dividing the numerator by O dividing the numerator and denominator by O dividing the denominator byWrite the equation in terms ot is rotated x'y'system using 8, the angle of rotation. Write the equation involving :5 and y' in standard form. xy=4,=45 The equation involving x\" and y\" in standard ionn is |:|. Write the equation in terms of a rotated x'yJ-systern using H, the angle of rotation. Write the equation involving x\" and y' in standard form. x2+$xy+y2-3=:3=45 The equation involving it\" and y' in standard form is |:|. Write the equation in terms of a rotated x'y'-system using I), the angle of rotation. Write the equation involving x\" and y' in standard form. 13):? + Eoxy- if - 391: U: E: =30\" The equation involving in\" and y' in standard form is |:|. Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. x2+5iiy+y2-?=D The appropriate rotation formulas are x = [:1 and y: |:|. (Simplify your answers. including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) '1'. Write the appropriate rotation formulas so that In a rotated System the equation has no x'y'-term. 12x2+1 3xy+2y2-1Q=D The appropriate rotation formulas are x = |:| and y = |:|. [Simplify your answersI including anyr radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) For the equation. 512 - 14):)I + 55:2 - 35 = 0. complete the following questions. a. Rewrite the equation in a rotated x'y'-system without an x'y'-term. Use the appropriate rotation formulae. b. Express the equation involving it\" and y' in the standard form of a oonio section. 6. Use the rotated system to graph the system. a. The equation in a rotated x'y'-svstem is :l. (Simplify your answer.) b. The equation involving :6 and y' in the standard form ofa oonic section is :I. [Use integers or fractions for any numbers in the equation.) G. Choose the correct graph below. C) B