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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 ENGLISH-CONIC SECTIONS-All Questions
  1. Find the points of contact Q and R of a tangent from the point P(2,3) ...

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  2. Two straight lines (y-b)=m1(x+a) and (y-b)=m2(x+a) are the tangents of...

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

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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 Aa n dT B are drawn to y^2=4a x . Th...

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  8. Tangent P Aa n dP B are drawn from the point P on the directrix of the...

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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 ( ...

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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 a parabola is along the line y=x and the distance of its v...

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  13. If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) wit...

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  14. If the normals at points t1 and t2 meet on the parabola, then (a) t1...

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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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