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A pair of tangents are drawn to the para...

A pair of tangents are drawn to the parabola `y^2=4a x` which are equally inclined to a straight line `y=m x+c ,` whose inclination to the axis is `alpha` . Prove that the locus of their point of intersection is the straight line `y=(x-a)tan2alphadot`

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the points of contact Q and R of tangents from the point P (2,3) ...

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  2. Two straight lines (y-b) =m(1)(x+a)and(y-b)=m(2)(x+a) are the tangents...

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  3. A pair of tangents are drawn to the parabola y^2=4a x which are equall...

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  4. Tangents are drawn from the point (-1,2) on the parabola y^(2)=4x. Fin...

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  5. Tangents are drawn to the parabola (x-3)^2+(y+4)^2=((3x-4y-6)^2)/(25) ...

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  6. Find the locus of point of intersection of tangents to the parabola y^...

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  7. Mutually perpendicular tangents T A and T B are drawn to y^2=4a x . T...

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  8. Tangents PA and PB are drawn from point P on the directrix to the para...

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  9. A square has one vertex at the vertex of the parabola y^2=4a x and the...

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  10. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

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  11. The equation of the line that passes through (10 ,-1) and is perpendic...

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  12. The axis of parabola is along the line y=x and the distance of its ver...

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  13. The locus of the circumcenter of a variable triangle having sides the ...

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  14. If the normals at P(t(1))andQ(t(2)) on the parabola meet on the same p...

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  15. From a point (sintheta,costheta), if three normals can be drawn to the...

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  16. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  17. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

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  18. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

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  19. If two normals to a parabola y^2 = 4ax intersect at right angles then ...

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  20. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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