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AP EAMCET · Maths · Ellipse

If the tangents drawn from a point \(P\) to the ellipse \(4 x^2+9 y^2-24 x+36 y=0\) are perpendicular, then the locus of \(P\) is

  1. A \(x^2+y^2-6 x+4 y+13=0\)
  2. B \(x^2+y^2-6 x+4 y-13=0\)
  3. C \(x^2+y^2=26\)
  4. D \(x^2+y^2+6 x-4 y-13=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x^2+y^2-6 x+4 y-13=0\)

Step-by-step Solution

Detailed explanation

Given, equation of ellipse is \[ \begin{aligned} & 4 x^2+9 y^2-24 x+36 y=0 \\ & \Rightarrow \quad 4\left(x^2-6 x+9\right)+9\left(y^2+4 y+4\right)-36-36=0 \\ & \Rightarrow \quad 4(x-3)^2+9(y+2)^2=72 \\ & \Rightarrow \quad \frac{(x-3)^2}{18}+\frac{(y+2)^2}{8}=1 \end{aligned} \]…