Ellipse 1 Question 4

5. The equation of the circle passing through the foci of the ellipse x216+y29=1 and having centre at (0,3) is

(2013 Main)

(a) x2+y26y7=0

(c) x2+y26y5=0

(b) x2+y26y+7=0

(d) x2+y26y+5=0

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Answer:

Correct Answer: 5. (c)

Solution:

  1. Given equation of ellipse is x216+y29=1

Here, a=4,b=3,e=191674

Foci =(±ae,0)=±4×74,0=(±7,0)

Radius of the circle, r=(ae)2+b2

=7+9=16=4

Now, equation of circle is

(x0)2+(y3)2=16x2+y26y7=0



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