Question

If the parabola has focus is (5, 0) and vertex is (3, 0) find its equation.
1. y² = 4x - 4
2. y2 = 8x + 4
3. y2 = 8x - 24
4. y2 = 4x + 12

Answer 1

Correct Answer - Option 3 : y2 = 8x - 24

Concept:

For a parabola symmetric about y-axis 

\(\rm (y-k)^2 = 4a(x-h)\)

Where vertex is (h, k) and focus is (h + a, k)

Calculation:

Given vertex is (3, 0)

h = 3, k = 0 

For focus = (5, 0)

h + a = 5

⇒ 3 + a = 5 

⇒ a = 2

So equation of parabola 

\(\rm (y-k)^2 = 4a(x-h)\)

⇒ \(\rm (y-0)^2 = 4\times2(x-3)\)

⇒ \(\boldsymbol{\rm y^2 = 8x-24}\)