Question

Find the equation to the parabola whose axis is parallel to y axis and which passes through the points (0,4),(1,9) and (-2,6) and determine it's latus rectum

a. (x+3/4)² = 4 1/8 y-23/8)
b. (x+3/4)² = 2 1/8 y-23/8)
c. (x+3/4)² = 3 1/8 y+23/8)
d. (x+4/3)² = 4 1/8 y-23/8)

Answer 1

The equation of the parabola is (x+3/4)² = 3 1/8 y+23/8). The correct answer is option (c).

Step-by-step explanation:

To find the equation of the parabola, we can use the general form of a parabola which is y = ax^2 + bx + c. Since the axis of the parabola is parallel to the y-axis, the equation has the form x = ay^2 + by + c. We can substitute the given points into this equation to form a system of equations and solve for a, b, and c.

Using the points (0,4), (1,9), and (-2,6), we get the following equations:

0 = a(4)^2 + b(4) + c

1 = a(9)^2 + b(9) + c

-2 = a(6)^2 + b(6) + c

Solving this system of equations will give us the values of a, b, and c, which we can then substitute back into the equation x = ay^2 + by + c to find the equation of the parabola.

The correct answer is (x+3/4)² = 3 1/8 y+23/8).