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AP EAMCET · Maths · Ellipse

If the ellipse \(4 x^2+9 y^2=36\) is confocal with a hyperbola whose length of the transverse axis is 2 , then the points of intersection of the ellipse and hyperbola lie on the circle

  1. A \(x^2+y^2=81\)
  2. B \(x^2+y^2=16\)
  3. C \(x^2+y^2=25\)
  4. D \(x^2+y^2=5\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(x^2+y^2=5\)

Step-by-step Solution

Detailed explanation

Ellipse : \(4 x^2+9 y^2=36\) ....(i) and Hyperbola \(=\frac{x^2}{1}-\frac{y^2}{b^2}=1\) \(\Rightarrow b^2 x^2-y^2=b^2\) As, they are confocal \(\therefore(a e)^2=a^2+b^2 \Rightarrow 5=1+b^2 \Rightarrow b^2=4\) So, hyperbola \(4 x^2-y^2=4\) .....(ii) Adding (i) and (ii),…