Q. A parabola is drawn with focus at $(3,\ 4)$ and vertex at the focus of the parabola $y^{2} - 12x - 4y + 4 = 0$. The equation of the parabola is
A) $x^{2} - 6x - 8y + 25 = 0$
B) $y^{2} - 8x - 6y + 25 = 0$
C) $x^{2} - 6x + 8y - 25 = 0$
D) $x^{2} + 6x - 8y - 25 = 0$
Explanation
(a)
${\because y}^{2} - 12x - 4y + 4 = 0$
$\Rightarrow {(y - 2)}^{2} = 12x$
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Its vertex is $(0,\ 2)$and $a = 3$,
Its focus is $(3,\ 2)$
Hence, for the required parabola; focus is $(3,\ 4)$,
Vertex is $(3,\ 2)$and $a = 2$
Hence, for the required parabola is
${(x - 3)}^{2} = 4(2)(y - 2)$
Or $x^{2} - 6x - 8y + 25 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.