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Consider the ellipse x^2/3 + y^2/1 = 1. ...

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)`

Text Solution

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`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
...
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