Question

Then equation of auxiliary circle of the ellipse \(16 x^{2}+25 y^{2}+32 x-100 y=284\) is
(A) \(x^{2}+y^{2}+2 x-4 y-20=0\)
(B) \(x^{2}+y^{2}+2 x-4 y=0\)
(C) \((x+1)^{2}+(y-2)^{2}=400\)
(D) \((x+1)^{2}+(y-2)^{2}=225\)

Answer 1

Ans: (A)
Simplifying the given equation, we have the ellipse as: \(\frac{(x+1)^{2}}{25}+\frac{(y-2)^{2}}{16}=1\)
So, the auxilliary circle is \((x+1)^{2}+(y-2)^{2}=25 \Rightarrow x^{2}+y^{2}+2 x-4 y-20=0\)