Question

Find the equation of the parabola whose axis is parallel to y-axis and which passes through the points (0,4) (1,9) and (4,5) and determine its latusrectum

Answer 1

Answer:

(x - 79/38)² = -12/19(y - 9889/912)

Step-by-step explanation:

Hi,

Let the center of the parabola be v(h, k)

Let latus rectum of the parabola be 4b

Equation of the parabola will be

(x - h)² = 4b(y - k)-------(1)

Given that parabola passes through (0, 4) , (1, 9) and (4, 5)

Substituting (0, 4) in (1), we get

h² = 4b(4 - k)---------(2)

Substituting (1, 9), we get

(1 - h)² = 4b(9 - k)---------(3)

Substituting (4, 5) in (1), we get

(4 - h)² = 4b(5 - k)-------(4)

(2) - (4) gives 8h - 16 = -4b-----(5)

(2) - (3) gives 2h - 1 = -20b------(6)

b = -3/19 and h = 79/38 and k = 9889/912

So, equation of parabola is (x - 79/38)² = -12/19(y - 9889/912)

Hope, it helps !