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The endpoints of two normal chords of a parabola are concyclic. Thenthe tangents at the feet of the normals will intersect attangent at vertex of the parabolaaxis of the paraboladirectrix of the parabolanone of theseA. tangent at vertex of the parabolaB. axis of the parabolaC. directrix of the parabolaD. none of these |
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Answer» Correct Answer - B (2) Let the concyclic points be `t_(1),t_(2),t_(3), and t_(4)` Then, `t_(1)+t_(2)+t_(3)+t_(4)=0` Here, `t_(1)andt_(3)` are the feet of the normal. So, `t_(2)=-t_(1)-(2)/(t_(1))andt_(4)=-t_(3)-(2)/(t_(3))` `:.t_(1)+t_(2)=-(2)/(t_(1))andt_(4)+t_(3)=-(2)/(t_(3))` Therefore, the lies on the intersection of tangents of tangents at `t_(1)andt_(3)` is `(at_(1)t_(3),a(t_(1)+t_(3)))-=(at_(1)t_(3),0)`. This point lies on the axis of the parabola. |
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