Question

The curve represented by the equation 4x2 + 16y2 - 24x - 32y - 12 = 0 is

• A. (A) a parabola
• B. (B) a pair of straight lines
• C. (C) an ellipse with eccentricity 1/2
• D. (D) an ellipse with eccentricity √3/2

Answer 1

Answer: (D)

(D) an ellipse with eccentricity √3/2

Answer 2

Explanation:
The given equation is4x2−24x+36+16y2−32y−12−36+16−16=0⇒(2x−6)2+(4y−4)2=64⇒(x−3)216+(y−1)24=1This represents an ellipse and a2=16,b2=4∴e=1−416=32