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Tangents are drawn at P and Q on ellipse x^2 /a^2 +y^2 /b^2 =1 to intersect in R(x1 , y1) and S is one of the two foci then ((RS)^2)/((PS)(QS)) is?

Tangents are drawn at P and Q on ellipse x^2 /a^2 +y^2 /b^2 =1 to intersect in R(x1 , y1) and S is one of the two foci then ((RS)^2)/((PS)(QS)) is?

Question Image
Grade:12th pass

1 Answers

Vikas TU
14148 Points
3 years ago
Dear Student,
the equation of any tangent to ellipse is
(x/a)cos theta +(y/b)sin theta =1
here, the tangent meets the R(a/ cos theta ,0) and S(0, b/sin theta)
or, a/cos theta= (RS^2)/(PS*QS)
=>also  (RS^2)/(PS*QS)= b/sin theta
cos^2 theta + sin^2 theta = (a^2 + b^2)/ (RS^2)/(PS*QS)
  • (RS^2)/(PS*QS)^2 RS^2)/(PS*QS)^2
so, RS^2)/(PS*QS)^2= sqrt(RS^2)/(PS*QS)^2) [Ans]
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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