Question

The equation of a parabola whose focus is (-3, 0) and the directrix is x + 5 = 0, is___

Answer 1

(x+3)^2 + y^2=((x+5)/1)^2
6x+9+y^2=10x+25
y^2=4(x+4) is your ans

Answer 2

Answer:

Step-by-step explanation:

According to definition of parabola , is is the locks of the points in that planes that are equidistant from both focus and directrix.

Given, focus : (-3,0)

directrix : x + 5 = 0

Let (x ,y) is the point on the parabola .

∴ distance of point from focus = distance of point from directrix

⇒ √{(x + 3)² + y²} = |x + 5|/√(1² + 0²)

⇒ √{(x + 3)² + y² } = |x + 5|

squaring both sides,

(x + 3)² + y² = (x + 5)²

⇒y² = (x + 5)² - (x + 3)²

⇒y² = (x + 5 - x - 3)(x + 5 + x + 3)

⇒y² = 2(2x + 8) = 4(x + 4)

Hence, equation of parabola is y² = 4(x + 4)