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MHT CET202617 April 2026Evening ShiftMathematicsApplication of DerivativesActual

The equation of the tangent to the curve y = 9 - 3x^2 at the point where the ordinate and abscissa equal is...

Options

  1. Ax - 3y + 3 = 0
  2. B3x - y - 3 = 0
  3. Cx + 3y - 6 = 0
  4. D3x + y - 6 = 0

Correct answer

D. 3x + y - 6 = 0

Step-by-step solution

Given curve is y = 9 - 3x^2 At the point where ordinate and abscissa are equal, y = x . Substituting y = x in the curve equation: x = 9 - 3x^2 Squaring both sides: x^2 = 9 - 3x^2 4x^2 = 9 x = 3 2 (since x 0 as y 0 ) Thus, the point of tangency is ( 3 2 , 3 2 ) . Differentiating the curve equation y^2 = 9 - 3x^2 with respect to x : 2y dy dx = -6x dy dx = -3x y At the point ( 3 2 , 3 2 ) , the slope of the tangent is: m = -3 ( 3 2 ) 3 2 = -3 The equation of the tangent is: y - 3 2 = -3 (x - 3 2 ) 2y - 3 = -6x + 9 6x

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