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AP EAMCET202316 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The points on the curve y^2=x+ x at which the normal is parallel to the Y-axis lie on

Options

  1. Aa line parallel to Y -axis
  2. Ba circle with centre at origin
  3. Ca parabola
  4. Da pair of lines bisecting the angle between the coordinate axes

Correct answer

C. a parabola

Step-by-step solution

The given curve is y^2=x+ x ...(i) d y d x = 1+ x 2 y Now, slope of the normal is m=- 1 ( d y d x ) =- 2 y 1+ x Normal is parallel to y -axis m= 1 0 aligned & - 2 y 1+ x = 1 0 1+ x=0 & x=-1 x= 1-(-1)^2 = 1-1 =0 aligned x=0 ...(ii) From eqns. (i) and (ii) : y^2=x+0 y^2=x which is a parabola.

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