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11. (0302 HC) All changes saved A right triangle is shown in the graph. y 1/ (1'. y) b (u.b) a .l' Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (a, b) and a point on the circle at (X, y). Show all necessary math work. (3 points) Part B: If (a, b) = (5, -2) and c = 10, determine the domain and range of the circle, (4 points) Part C: Is the point (1 O, 2) inside the border of the circle if (a. b) = (5. 2) and c =10? Explain using mathematical evidence. (3 points) 3' (03.02 LC) Which of the following is the equation of the circle with center C and a point P on the circle, as shown in the graph? (3 points) 7. (03.03 MC) The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (1, 5) and top of the bulb is at (1, 1)? (3 points) O ( x+ 1) 2 = 20 (y + 5 ) O ( x + 1) 2 = 16 (y + 5 ) O ( x - 1) 2 = -20(1 - 5) O ( x - 1) 2 = -16 (1 - 5)12. (03.03 HC) A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 20 mm halfway across a horizontal distance of 160 mm. Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points) Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)5. (03.02 MC) The circle x2 + y2 12X + 6y 19 = 0 is translated one unit right and two units down, Which is the radius and center of the translated circle? (3 points) O Center (6, 3); r = 8 0 Center (7, 5); r = 8 0 Center (6, -3); r = 64 0 Center (7, 5); r = 64 6. (03.02 MC) The signal of Micha's Wi-Fi router covers a circular area, whose border is modeled by the equation (X 5)2 +y2 = r2, She discovers the boundary is located at (9, 3). What is the radius of the signal? (3 points) 090 10. (03.03 MC) The flight path of a rocket, launched from the ground, is modeled by y = 0.5(20x - x2), where y is the height of the rocket in meters from the ground and x is the time in seconds after it was launched. Find the vertex of the parabola and explain what it represents in terms of the context. (3 points) O (20, 0); rocket lands at 0 feet after 20 seconds O (10, 50); rocket reaches maximum height of 50 feet after 10 seconds (10, 50); rocket reaches maximum height of 10 feet after 50 seconds O (20, 0); rocket reaches 20 feet after 0 seconds9. (03.03 MC) A parabola is modeled with the equation x2- 6x + 4y - 19 = 0. Which is the domain and range of the parabola? (3 points) O D: (-00, 00); R: [7, 00) O D: (-00, 00); R: (-00, 7] O D: (-00, 71; R: (-00, 00) O D: [7, 00); R: (-00, 00)1. (03.01 LC) A parabola is formed when a plane slices through a cone Which of the following describes the relationship between the plane and the cone? (3 points) 0 The plane is parallel to the base of the cone. 0 The plane is perpendicular to the base of the cone 0 The plane is parallel to the slant edge of the cone and intersects the base of the cone 0 The plane is at a slight angle with respect to the base of the cone. but does not intersect it. 2. (0301 LC) Which of the following is not created when a plane slices through a cone? (3 points)