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

Options

A. a parabola
B. a pair of stright lines
C. an ellipse with eccentricity `(1)/(2)`
D. an ellipse with eccentricity `(sqrt(3))/(2)`

Answer

D

Explanation

we have ,
`4x^(2)+16y^(2)-24x-24x-32y-12=0`
` implies 4(x^(2) -6x+9)+16(y^(2)-2y+1)=64`
`implies ((x-3)^(2))/(4^(2))+((y-1)^(2))/(2^(2))=1`
Clearly , it represents an ellipse with eccentricity e given by
`e=sqrt(1-(4)/(16))=(sqrt(3))/(2)`