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Question: The auxiliary circle of a family of ellipse passes through origin and makes intercept of 8 and 6 uni...

The auxiliary circle of a family of ellipse passes through origin and makes intercept of 8 and 6 units on x-axis and y-axis respectively. If eccentricity of all such family is 12\frac{1}{2}then locus of focus will be-

A

x216\frac{x^{2}}{16}+ y29\frac{y^{2}}{9}= 25

B

4x2 + 4y2 –32x –24y + 75 = 0

C

x216\frac{x^{2}}{16}– y29\frac{y^{2}}{9}= 25

D

None of these

Answer

4x2 + 4y2 –32x –24y + 75 = 0

Explanation

Solution

Centre is (4, 3) and distance of focus from

centre is ae = 52\frac{5}{2}

\ locus is (x – 4)2 + (y – 3)2 = 254\frac{25}{4}