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Consider the ellipse `x^2/3 + y^2/1 = 1`. Let P,Q,R,S be four points on the ellipse such that the normal drawn from these points are con current at (2,2) then the centre of the conic on which these 4 points lie is (A) P,Q,R,S lie on the given ellipse (B) `(3,-1)` (C) `(3,1)` (D) `(0,0)` |
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Answer» `N=(a^2x)/x_1-(b^2y)/y_1=a^2-b^2` `=(2a^2)/x_1-(b^2 2/y_1)=a^2-b^2` `=3/x_1-1/y_1=1` `3y_1-x_1-x_1y_1-(1)` `3y_2-x_2=x_2y_2-(2)` `xy+x-3y=0` differentiate with respect to x y+1=0,y=-1 x+(-3)=0,x=3 (3,-1) option b is correct. |
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