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If chords of contact of the tangent from two points
$(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ are at right angles, then $\frac{x_{1} x_{2}}{a^{2}} \times \frac{y_{1} y_{2}}{b^{2}}$ is equal to

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a2b2

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−a4b4

b4a4

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detailed solution

Correct option is C

Chords of contacts are xx1a2+yy1b2=1 and xx2a2+yy2b2=1Since they are at right angles−b2a2×x2y2×−b2a2×x1y1=−1⇒x1x2y1y2=−a4b4

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If chords of contact of the tangent from two points x1, y1 and x2, y2 to the ellipse x2a2+y2b2=1 are at right angles, then x1x2a2×y1y2b2 is equal to

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Ready to Test Your Skills?

free study material

If chords of contact of the tangent from two points
$(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ are at right angles, then $\frac{x_{1} x_{2}}{a^{2}} \times \frac{y_{1} y_{2}}{b^{2}}$ is equal to