Find the equation of the parabola if
Focus is at $(0, - 3)$ and the vertex is at $(- 1, - 3)$

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Solution

focus (0,-3) &
vertex (-1,-3)
Equation of parabola,
$y^{2} = 4 a x . . . (1)$
$x = - 1, y = - 3, a = - 3$
Putting these values in $e q^{n}$ (1), we get
$(y + 3)^{2} = 4 (- 3) (x + 1)$
$y^{2} + 9 + 6 y + 12 x + 12 = 0$
$y^{2} + 6 y + 12 x + 21 = 0$

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Similar questions

Find the equation of the parabola,if

(i) the focus is at (-6,-6) and the vertex is at (-2,2)

(ii) the focus is at (0,-3) and the vertex is at (0,0)

(iii) the focus is at (0,-3) and the vertex is at (-1,-3)

(iv) the focus is at (a,0) and the vertex is at (a',0)

(v) the focus is at (0,0) and vertex is at the intersection of the lines x+y=1 and x-y=3.

x + 3 = 0

(1, 1)

(3, 1)

(0, 0)

x - y + 1 = 0

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