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Question

Question: The auxilary circle of the ellipse 9x<sup>2</sup> + 25y<sup>2</sup>-18x-100y-116=0...

The auxilary circle of the ellipse 9x2 + 25y2-18x-100y-116=0

A

(x+1)2 + (y+2)2 = 9

B

(x+1)2+(y+1)2=25

C

(x-1)2+(y-2)2 = 9

D

(x-1)2+(y-2)2 = 25

Answer

(x-1)2+(y-2)2 = 25

Explanation

Solution

The given ellipse can put in the form of

(x1)225+(y2)29=1\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{9} = 1, Here (α, β) = (1, 2) is the centre.

The equation of auxilary circle is (x - α)2 + (y-β)2 = a2

(x-1)2 + (y-2)2 = 25