WBJEE · Maths · Ellipse
The 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 & Solution
Correct Answer
(A) \(x^{2}+y^{2}+2 x-4 y-20=0\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse is \[ 16 x^{2}+25 y^{2}+32 x-100 y=284 \] Simplifying the given equation, we have ellipse as \[ \frac{(x+1)^{2}}{25}+\frac{(y-2)^{2}}{16}=1 \] So, the auxiliary equation of circle is…
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