MHT CET202311 May 2023Evening ShiftMathematicsApplication of DerivativesActual
The equation of the tangent to the curve y= 9-2 x^2 , at the point where the ordinate and abscissa are equal, is
Options
- A2 x+y+ 3 =0
- B2 x+y+3 3 =0
- C2 x-y-3 3 =0
- D2 x+y-3 3 =0
Correct answer
D. 2 x+y-3 3 =0
Step-by-step solution
Given curve is y= 9-2 x^2 If ordinate and abscissa are equal, we get y=x . Equation of the curve becomes x^2=9-2 x^2 x= 3 If x=- 3 , then y= 9-2(3) = 3 In this case, x y . Hence, x - 3 x= 3 and y= 3 Slope of the tangent to the given curve is aligned & 2 y d y ~d x =-4 x & at ( 3 , 3 ), d y ~d x =-2 aligned Equation of the required tangent is aligned & (y- 3 )=-2(x- 3 ) & i.e., 2 x+y-3 3 =0 aligned