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AP EAMCET · Maths · Ellipse

If the line joining the points \(A(\alpha)\) and \(B(\beta)\) on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) is a focal chord, then one possible value of \(\cot \frac{\alpha}{2} \cdot \cot \frac{\beta}{2}\) is

  1. A -3
  2. B 3
  3. C -9
  4. D 9
Verified Solution

Answer & Solution

Correct Answer

(C) -9

Step-by-step Solution

Detailed explanation

Since equation of chord joining the points \(A(\alpha)\) and \(B(\beta)\) on the ellipse \(\frac{x^2}{25}+\frac{y^2}{9}=1\) is \(\frac{x}{5} \cos \frac{\alpha+\beta}{2}+\frac{y}{3} \sin \frac{\alpha+\beta}{2}=\cos \frac{\alpha-\beta}{2}\) ...(i) \(\because\) Chord (i) is the…