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MHT CET202613 April 2026Morning ShiftMathematicsParabolaActual

A point on the parabola y^2 = 36 5 x at which the ordinate increases at thrice the rate of the abscissa is .....

Options

  1. A( 6 5 , 1 5 )
  2. B( 1 5 , 6 5 )
  3. C(5, 6)
  4. D( 3 5 , 9 5 )

Correct answer

B. ( 1 5 , 6 5 )

Step-by-step solution

Given the equation of the parabola: y^2 = 36 5 x Differentiating both sides with respect to time t : 2y dy dt = 36 5 dx dt It is given that the ordinate increases at thrice the rate of the abscissa, so: dy dt = 3 dx dt Substituting this into the differentiated equation: 2y (3 dx dt ) = 36 5 dx dt 6y = 36 5 y = 6 5 Substituting y = 6 5 into the equation of the parabola to find x : ( 6 5 )^2 = 36 5 x 36 25 = 36 5 x x = 1 5 The required point is ( 1 5 , 6 5 ) .

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