Q. The curve represented by the equation $4x^{2} + 16y^{2} - 24x - 32y - 12 = 0\$is
A) A parabola
B) A pair of straight lines
C) An ellipse with eccentricity 1/2
D) An ellipse with eccentricity $\sqrt{3}/2$
Explanation
(d)
Given equation can be rewritten as
$\frac{(x - 3)^{2}}{16} + \frac{(y - 1)^{2}}{4} = 1$
This represents an ellipse
$e = \sqrt{1 - \frac{4}{16}} = \frac{\sqrt{3}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.