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Q.

The equation of the parabola $x^{2} - 4 x - 4 y + 16 = 0$ is transformed to $x^{2} = 4 y$ . When the origin is shifted to $(h, k),$ then the values of h, k are

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a

$k = 2$

b

$k = 3$

c

$h = - 2$

d

$h = 2$

answer is A, C.

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Detailed Solution

$h = 2, k = 3$

$x = X + 2, y = Y + 3$

${(X + 2)}^{2} - 4 (X + 2) - 4 (y + 3) + 16 = 0$

$X^{2} + 4 + 4 Y - 4 X - 8 - 4 Y - 12 + 16 = 0$

$X^{2} = 4 y$

$h = 2, k = 3$

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The equation of the parabola x2−4x−4y+16=0is transformed to x2=4y. When the origin is shifted to (h, k),then the values of h, k are