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The co-ordinates of end points of a foca...

The co-ordinates of end points of a focal chord of an ellipse are `(x_1,y_1)`and `(x_2,y_2)`.Prove that `y_1y_2+4x_1x_2=0`

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The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

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If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

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UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2017-EXERCISE
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