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AP EAMCET20225 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If the slope of the tangent at a point ( x , y ) on a curve is y-4 x-3 and the curve passes through (4,3) , then the point where it cuts the line y = x is

Options

  1. A(1,1)
  2. B(3,3)
  3. C( 7 2 , 7 2 )
  4. D(- 5 2 ,- 5 2 )

Correct answer

C. ( 7 2 , 7 2 )

Step-by-step solution

d y d x = y-4 x-3 d x x-3 = d y y-4 (x-3 )= (|y-4|)+c as curve passes through (4,3) 1= 1+c c=0 |x-3|- |y-4|=0 | x-3 y-4 |=0 | x-3 y-4 |=e^0=1 |x-3|=|y-4| As we have to check at y=x |x-3|=x-4 3-x=x-4 x=y= 7 2 ( 7 2 , 7 2 )

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