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AP EAMCET202021 Sep 2020Morning ShiftMathematicsEllipseActual

For the ellipse ( x^2 18 + y^2 32 =1 ), if a tangent with slope ( -4 3 ) intersects the major and minor axes at (P ) and (Q ) respectively. Find (P ) and (Q ).

Options

  1. A(P(0,8), Q(6,0) )
  2. B(P(0,6), Q(8,0) )
  3. C(P(3 2 , 0), Q(0,4 2 ) )
  4. D(P(0,3 2 ), Q(4 2 , 0) )

Correct answer

A. (P(0,8), Q(6,0) )

Step-by-step solution

Equation of tangent to the ellipse ( x^2 18 + y^2 32 =1 ) having slope (- 4 3 ) is ( array rlrl & & & y=- 4 3 x 18 ( 16 9 )+32 & & y & =- 4 3 x 8 & 4 x+3 y & = 24 array ) The tangent (4 x+3 y=24 ) cuts the major and minor axes at point (P(0,8) ) and (Q(6,0) ). And the tangent (4 x+3 y=-24 ) cuts the major and minor axes at point (P(0,-8) ) and (Q(-6,0) ).

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