Question

If the focus of a parabola is (0 -3) and its directrix is y = 3 , then its equation is

Clear and Complete Answer Required

Answer 1

Answer:

• Focus = (0 , -3)
• Directix = y = 3 OR y - 3 = 0 OR 0x + 1y - 3 = 0.

Let P(x,y) be the point on the parabola, such that it is equidistant. Then,

$\sf (x - 0)^2 + (y -(-3))^2 = \dfrac{(y-3)}{0^2+1^2}$

(I used the distance formula and the perpendicular distance formula.)

Further simplifying, we get:

$\sf x^2 + y^2+9+ 6y = y-3$

$\sf x^2 + y^2+12+ 5y= 0$

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