The normal to the curve yx 2x 3 x 6 at the point where the curve intersects the y axis passes through the point JEE MAINS Mathematics 2017

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The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point :-JEE MAINS-Mathematics-2017

(1)(1/2,1/3)
(2)(-1/2,-1/2) 
(3)(1/2,1/2)
(4)(1/2,-1/3)


By:Purnima

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 y=x+6/(x-2)(x-3)
 Point of intersection with y-axis is (0,1).
 y'=((x^2-5x+6)(1)-(x+6)(2x-5))/(x^2-5x+6)^2
 y'= 1 at point (0, 1)
 Slope of normal is –1
 Hence equation of normal is x + y = 1
 Thus,(1/2,1/2) satisfy it.

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