Question

The curve represented by the equation 4x² + 16y² - 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 √3/2

Answer 1

The Correct Option is D

Explanation:
The given equation is$$\begin{array}{l}4x^2-24x+36+16y^2-32y-12-36+16-16=0\\ \Rightarrow (2x-6{)}^2+(4y-4{)}^2=64\\ \Rightarrow \frac{(x-3{)}^2}{16}+\frac{(y-1{)}^2}{4}=1\end{array}$$This represents an ellipse and $a^2=16,b^2=4$$\therefore$$$e=\sqrt{1-\frac{4}{16}}=\frac{\sqrt{3}}{2}$$