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The line `x-y=1`intersects the parabola `y^2=4x`at `A`and `B`. Normals at `Aa n dB`intersect at `Cdot`If `D`is the point at which line `C D`is normal to the parabola, then the coordinates of `D`are`(4,-4)`(b) `(4,4)``(-4,-4)`(d) none of theseA. (4,-4)B. (4,4)C. (-4,-4)D. none of these |
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Answer» Correct Answer - B (2) solving the line y=x-1 and the parabola `y^(2)=4x`, we have `(x-1)^(2)=x` `orx^(2)-6x+1=0` `orx=3pmsqrt(8)` `:.y=2pmsqrt(8)` Suppose point D is `(X_(3),y_(3))`. Then, `y_(1)+y_(2)+y_(3)=0` `or2+sqrt(8)+2-sqrt(8)+y_(3)=0` `ory_(3)=-4` Then `x_(3)=4`. Therefore, the point is (4,4). |
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