Reduce the following equation of the parabola to the standard form:
(a) $4 x - y^{2} + 2 y + 13 = 0$
(b) $x^{2} + 4 x + 16 y + 52 = 0$

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Solution

(a) $4 x - y^{2} + 2 y + 13 = 0$

$4 x - [y^{2} - 2 y + 1] + 14 = 0$

$\Rightarrow (y - 1)^{2} = 4 x + 14$

$\Rightarrow (y - 1)^{2} = 4 (x + 7 / 2)$

(b) $x^{2} + 4 x + 16 y + 52 = 0$

$\Rightarrow x^{2} + 4 x + 4 + 16 y + 48 = 0$

$\Rightarrow (x + 2)^{2} = - 16 (y + 3)$

these are the standard questions of parabola

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List-I	List-II
A) Vertex of the parabola $y^{2} - x + 4 y + 5 = 0$	p) (1,4)
B) Focus of the parabola $x^{2} - 2 x - 12 y + 13 = 0$	q). (1,-2)
C) The directrix of the parabola $x^{2} + 4 x + 2 y - 8 = 0$	r) 2y-13=0
D) Normal at (1,1) to $y^{2} = x$	s) 2x+y-3=0

x^{2} + y^{2} + 4 x + 6 y + 13 = 0

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