Precalc!! PLEASE SHOW THE WORK Question> 1. If a parabola's focus is at (-2,5) and directrix is at y = -1, what is the vertex form of the equation representing this parabola Answers> A. y = -1/12(x - 2)^2 - 5 B. y= 1/4(x - 3)^2 + 3 C. y = 1/4(x + 5)^2 + 2 D. y = 1/12(x+2)^2 + 2 Question> 2. What is the keyword Asian of the para bola shown below, given the focus at F(-2,5) and the directrix y = 9? Identify the vertex and the equation of the axis of symmetry of the parabola. (PICTURE WILL BE SENT IN MESSAGE) Answers> A. y= 1/8(x + 2)^2 + 7; vertex (-2,7); axis of symmetry is x = -2 B. y = -1/8(x + 2)^2 + 7; vertex (-2, 7); axis of symmetry is x = -2 C. y = 1/4(x - 2)^2 + 7; vertex (2,7); axis of symmetry is x = 5 D. y = -1/4(x - 2)^2 + 7; vertex (2,7); axis of symmetry is x = 2 Question> 3. The equation of a quadratic relation is y = -1/16(x - 1)^2 + 3. Every point on this conic is equidistant from the focal point (a,b) and the line defined by y = c. Answers> A. 8 B. 9 C. 10 D. 7 Question> 4. Find the centre and radius of the circle x^2 + y^2 - 4x + 6y - 23 = 0. Answers> A. centre (2,-3), radius sqrt6 B. centre (-2,-3), radius sqrt6 C. centre (3,2), radius sqrt6 D. centre (2,-3), radius 6 Question> 5. What is the equation of the circle with centre (1/2,0) and radius 6? Answers> A. (2x - 1)^2/2 + y^2 = 6 B. (2x - 1)^2/4 + y^2 = 36 C. (2x - 1)^2/4 + y^2 = 6 D. (2x - 1)^2/2 + y^2 = 36 Question> 6. Write the equation of a circle with centre (5,-2) which is tangent to the y-axis. Answers> A. (x - 5)^2 + (y + 2)^2 = 25 B. (x - 5)^2 + (y - 2)^2 = 25 C. (x + 5)^2 + (y - 2)^2 = 5 D. (x + 5)^2 + (y - 2)^2 = 25 Question> 7. what is the equation of the given ellipse? (1,2) (5,0.5) (Picture will be in message) Answers> A. (x - 1)^2/ 16 + 4(y - 1/2)^2/9 = 1 B. (x - 1)^2/16 + (y - 1/2)^2/4 = 1 C. (x - 1)^2/4 + 2(y - 1/2)^2 = 1 D. (x + 1)^2/16 + 4(y + 1/2) ^2 = 1 Question> 8. The point (k,3) lies on the ellipse x^2/32 + y^2/18 = 1. Which of the following could be a value for K? Answers> A. 6 B. 3sqrt2 C. 4 D. 8sqrt2 Question> 9. An ellipse has centre (0,0) and vertices on the y-axis. The minor axis has length 10 and the major axis has length 14. Find the equation of the ellipse. Answers> A. x^2/100 + y^2/196 = 1 B. x^2/25 + y^2/49 = 1 C. c^2/49 + y^2/25 = 1 D. x^2/7 + y^2/5 = 1 Question> 10. Write the equation of the hyperbola with centre at (-3,-1), vertex at (-6,-1) one asymptote with equation 2x - 3y = -9 Answers> A. (x + 3)^2/9 - (y + 1)^2/4 = 1 B. (x + 3)^2/4 - (y - 1)^2/9 = 1 C. (x - 3)^2/9 - (y + 1)^2/4 = 1 D. (x - 3)^2/4 - (y + 1)^2/9 = 1