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JEE Main20254 Apr 2025Evening ShiftMathematicsParabolaActual

A line passing through the point A (-2,0) , touches the parabola P: y^2=x-2 at the point B in the first quadrant. The area, of the region bounded by the line AB , parabola P and the x -axis, is :-

Options

  1. A7 3
  2. B2
  3. C8 3
  4. D3

Correct answer

C. 8 3

Step-by-step solution

Tangent aligned & y=m(x+2) & y^2=x-2 & (m(n+2))^2=n-2 & m^2 x^2+ (4 m^2-1 ) x+ (4 m^2+2 )=0 & D=0 & (4 m^2-1 )^2-4 m^2 (4 m^2+2 )=0 & m= 1 4 & y= 1 4 (n+2) aligned and point of tangency (6,2) aligned & Area A= ₀^2 ( (y^2+2 )-(4 y-2) ) d y & A= 8 3 aligned option (3)

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