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AP EAMCET20226 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A2 x+y-3 3 =0
  2. B2 x+y+3 3 =0
  3. C2 x-y-3 3 =0
  4. D2 x-y+3 3 =0

Correct answer

A. 2 x+y-3 3 =0

Step-by-step solution

We have curve y= 9-2 x^2 Let ( x ₁, y ₁ ) be any point such that x ₁= y ₁ on the curve x ₁ ^2= g -2 x ₁ ^2 x ₁= 3 or y ₁= 3 9-2 x 2 is always + ve y >0 point is ( 3 , 3 ) now slope dy dx = -2 x y at ( 3 , 3 ) will be dy dx =-2 now equation of tangent is aligned & (y- 3 )=-2(x-2) & 2 x+y-3 3 =0 aligned

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