Question

The curve represented by the equation $4 x^2+16 y^2-24 x-32 y-12=0$ is

(a) a parabola

(b) a pair of straight lines

(c) an ellipse with eccentricity $1 / 2$

(d) an ellipse with eccent ity $\sqrt{3} / 2$

Answer 1

The given equation can be rewritten as

$\frac{(x-3)^2}{16}+\frac{(y-1)^2}{4}=1$

This represents an ellipse and $a^2=16, b^2=4$

$\therefore \quad e=\sqrt{1-\frac{4}{16}}=\frac{\sqrt{3}}{2}$

So, The correct option of this question will be (D).