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

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Correct answer: A. (a) ∵y=x^2+5 … … … … … … (i ) ⇒y^ '=2x Equation of tangent line at point A (-2 ,9 ) : (y-9 )= (2x-2 ) (x+2 ) ⇒y-9=-4x-8 ⇒y=-4x+1 … … … … . . ( ii ) let coordinate of C is (x^ ' ,y^ ' ) Then, 6-y^ '1-x^ '=-4 ⇒6-y^ '=-4+4x^ ' ⇒y^ '+4x^ '=10…………..(iii) ∵C (x^ ' ,y^ ' ) lies on equation (i), we get y^ '=x^ '2+5………….(iv) Using eq . (iv) in equation (iii), we get x^ '2+5+4x^ '=10 ⇒x^ '2+4x^ '-5=0 ⇒x^ '=-5 ,1 when x^ '=-5 ⇒y^ '=25+5=30 Then C ≡ (-5 ,30 ).

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

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