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AP EAMCET202318 May 2023Evening ShiftMathematicsParabolaActual

A(-2,9) and B(1,6) are two points on the curve y=x^2+5 . The coordinates of the point C on the curve such that the tangent drawn at A is parallel to the chord BC , is

Options

  1. A(-5,30)
  2. B(0,5)
  3. C(-9,86)
  4. D(6,41)

Correct answer

A. (-5,30)

Step-by-step solution

aligned & y=x^2+5 & y^ =2 x aligned Equation of tangent line at point A(-2,9) : aligned & (y-9)=(2 x-2)(x+2) & y-9=-4 x-8 y=-4 x+1 aligned let coordinate of C is ( x ^ , y ^ ) Then, 6-y^ 1-x^ =-4 6-y^ =-4+4 x^ y^ +4 x^ =10 C ( x ^ , y ^ ) lies on equation (i), we get y ^ = x ^ 2 +5 Using eq ^ n (iv) in equation (iii), we get aligned & x ^ 2 +5+4 x ^ =10 x ^ 2 +4 x ^ -5=0 x ^ =-5,1 & when x ^ =-5 y ^ =25+5=30 & Then C (-5,30) aligned

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