the equation of the circle passing through the foci of the ellipse `(x^(2))/(16)+(y^(2))/(9)=1` and having centre at (0,3) is

Options

A. `x^(2)+y^(2)-6y-7=0`
B. `x^(2)+y^(2)-6y+7=0`
C. `x^(2)+y^(2)-6y-5=0`
D. `x^(2)+y^(2)-6y+5=0`

Answer

A

Explanation

Here, `a=4,b=3`
and `e=sqrt(1-(9)/(16))=(sqrt(7))/(4)`
`:.` Foci is
`( pm ae, 0)= ( pm 4xx(sqrt(7))/(4),0) = (pm sqrt(7) ,0)`
`:.` Radius of the circle,
`r= sqrt((ae)^(2)+b^(2))=sqrt(7+9)=sqrt(16)=4`
Equation of circle is
`(x0-0)^(2)+(y-3)^(2)=4^(2)`
`rArr x^(2)+y^(2)-6y-7=0`