SOLUTION: Equation:y²=-8x is in the standard form y²=4ax (horizontal parabola), where the Formula for Latus Rectum: The length of the latus rectum is 4a . Solution Equation: For a parabola with vertex at(0, 0) and focus(0, −p), the equation is x² = -4py Given: Focus(0, −3) impliesp = 3. Solution: Equation is x²=−12y. Answer: c)x²=-12y. solution: Equation: x²=4y is in the form x² = 4ay where a = 1 Solution: Length of the latus rectum = 4a = 4 Answer: b) 4 Property: The eccentricity of a parabola is always 1. Equation: y² = 4ax, with4a = 16 , so a = 4. Answer: a) 16 units Directrix: x = −p, where p = 2. Equation:x² = 12y is a vertical parabola with symmetry about the y-axis. Focus: The focus is (a, 0) . Focus and Vertex: The distance between the vertex and focus is 3, so 4p = 12 , giving p=3 Equation: The general form for a parabola parallel to the x-axis is . Equation:4a = 4 , so a = 1 . Equation: y =2 −4ax with a = 1, and the directrix is x = −1. Equation: 4a = 8, so a = 2. Equation 4a = 16 so a = 4 Solution: Length of the latus rectum 4a= 16. Answer: d) 16 units
Results
#1. Vertex of parabola y²=-8x is:
vertex is at .(0,0)
Solution: The vertex is the origin.
Answer: a) (0, 0)#2. For the parabola ,y²=4ax if the length of the latus rectum is 8, then the value of a is:
Given: Length of the latus rectum = 8.
Solution:4a=8 , so a=2.
Answer: a)2#3. The equation of the parabola with vertex at the origin and focus at (0,-3) is:
#4. The length of the latus rectum of the parabola x²= 4y
#5. The coordinates of the focus of the parabola x²=16 y are:
#6. the eccentricity of a parabola is always
Answer: b) 1#7. The length of latus rectum of the parabola y²=16x is:
Solution: Length of the latus rectum 4a = 16.#8. The equation of the parabola with vertex at the origin and directrix x=-2 is:
Equation: The parabola’s equation is y =2 4px = 8x.
Answer: a)y² = 8x#9. The axis of symmetry of the parabola x²=12y is:
Answer: b) y-axis#10. For the parabola y²=4ax the coordinates of the focus are:
Solution: Focus = (a, 0).
Answer: a)(a, 0)#11. the equation of the parabola with vertex at (3,-2) and focus at (3,1) is:
.
Equation:(x − 3) =2 12(y 2) .
Answer: b)(x − 3) =2 12(y 2)#12. If the axis of a parabola is parallel to x-axis then generalform oth the equation is:
Answer: a)y² = 4ax#13. For the parabola y²=4x the length of latusrectum is:
Solution: Length of the latus rectum = .
Answer: a) 4#14. The equation of the directix of the parabola y²=-4x is :
Answer: b) x = −1#15. The focus of the parabola x²=8y is at:
Focus: Focus is (0, a) = (0, 2).
Answer: a)= (0, 2)#16. For the parabola y²=16x the length of the latus rectum is:
#17. The equation of the parabola with vertex 0,0 and directrix x=-3 is:
#18. The parabola y²=16x opens
#19. The equation y²=4px represents a parabola if:
#20. The tangent at a point p(x1,y1) on the parabola y²=4ax is