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The equation of the circle passing throu...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A
given equation of ellipse of ellipse is `(x^(2))/(16)+(y^(2))/(9)=1`

Here` a=4,b=3, e=sqrt(1-(9)/(16))implies (sqrt(7))/(4)`
` therefore `Foci `=(+_4xx(sqrt(7))/(4),0)=(+_sqrt(7),0)`
Radius of the circle is , `r= sqrt((ae)^(2)+b^(2))`
`=sqrt(7+9)=sqrt(16)=4`
NOw , equation of circle is
`(x-o)^(2)+(y-3)^(2)=16`
`therefore x^(2)+y^(2)-6y-7=0`
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