Question

The equation of parabola with the focus (2, 0) and directrix as x + 2 = 0 is ?
1. x2 = - 8y
2. x2 = 8y
3. y2 = - 8x
4. y2 = 8x

Answer 1

Correct Answer - Option 4 : y2 = 8x

Concept:

If a point (x, y) lies on Parabola, then its distance from focus is always equal to its distance from directrix. 

Calculation:

Let a point (x, y) lie on parabola, then its distance from focus is always equal to its distance from directrix. 

i.e. Distance between (x, y) and focus (2, 0) = Distance between (x, y) and directrix i.e x + 2 =0

⇒ \(\rm \sqrt{(x-2)^2 + (y-0)^2}= \frac{x+2}{\sqrt{1^2 +0^2}}\) 

⇒ \(\rm \sqrt{(x-2)^2 + y^2}= \frac{x+2}{\sqrt{1}}\) 

By squaring both sides we get,

⇒ \(\rm {(x-2)^2 + y^2}= \frac{(x+2)^2}{{1}}\)

⇒ \(\rm {(x-2)^2 + y^2}= {(x+2)^2}\)

⇒ x² - 4x + 4 + y² = x² + 4x + 4

⇒ - 4x + y2 = 4x 

⇒ y2 = 8x 

Hence, option 4 is correct.