Q. A parabola is drawn with its 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) $y^{2} - 8x + 6y + 25 = 0$
B) $y^{2} - 6x + 8y - 25 = 0$
C) $x^{2} - 6x - 8y + 25 = 0$
D) $x^{2} + 6x - 8y - 25 = 0$
Explanation
(c)
Given equation can be rewritten as.
$(y - 2)^{2} = 12x\$
Here, vertex and focus are $(0,\ 2)$and (3, 2)
$\therefore$ Vertex of the required parabola is (3, 2) and focus is (3, 4). The axis of symmetry is $x = 3\$and latusrectum$= 4 \times 2 = 8$
Hence, required equation is
$(x - 3)^{2} = 8(y - 2)$
$\Rightarrow \ x^{2} - 6x - 8y + 25 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.