Question

find the equation of a parabola whose focus is (-3,0) and directrix is x+4=0

Answer 1

Answer:

y² = 2x + 7 is the equation of the parabola.

Step-by-step explanation:

Hi,

If a point moves in such a way that the distance from fixed point

is equal to the distance from the fixed line, then the locus is

known as parabola, and fixed point is focus and the fixed line is

the directrix.

Given focus S(-3, 0)

Directrix , L = x + 4 = 0

Hence, using the definition of parabola, if P(x, y ) is any general point, then

SP = PL

=>√(x + 3)² + y² = | x + 4|

Squaring on both sides, we get

(x + 3)² + y² = (x + 4)²

=> y² = ( x + 4)² - (x + 3)²

=> y² = 2x + 7 is the equation of the parabola.

Hope , it helps !