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The orthocenter of a triangle formed by 3 tangents to a parabola `y^2=4ax` lies on

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Prove that the area of triangle formed by the tangents to the parabola y^(2)=4ax from the point (x_(1),y_(1)) and the chord of contact is 1/(2a)(y_(1)^(2)-4ax_(1))^(3//2) sq. units.

The locus of centroid of triangle formed by a tangent to the parabola y^(2) = 36x with coordinate axes is

The triangle formed by the tangents to a parabola y^(2)=4ax at the ends of the latus rectum and the double ordinate through the focus is

The locus of the Orthocentre of the triangle formed by three tangents of the parabola (4x-3)^(2)=-64(2y+1) is

Equation of tangent to parabola y^(2)=4ax

The triangle formed by the tangent to the parabola y^2=4x at the point whose abscissa lies in the interval [a^2,4a^2] , the ordinate and the X-axis, has greatest area equal to :

If a triangle is formed by any three tangents of the parabola y^(2)=4ax, two of whose vertices lie on the parabola x^(2)=4by, then find the locus of the third vertex

The area of the triangle formed by the tangent and the normal to the parabola y^(2)=4ax, both drawn at the same end of the latus rectum, and the axis of the parabola is 2sqrt(2)a^(2)(b)2a^(2)4a^(2)(d) none of these

A DAS GUPTA-Parabola-EXERCISE
  1. If (a^2, a -2) be a point interior to the region of the parabola y^2...

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  2. Show that the tangents at the extremities of any focal chord of a par...

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  3. The orthocenter of a triangle formed by 3 tangents to a parabola y^2=4...

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  4. Tangents are drawn from any point on the line x+4a=0 to the parabola y...

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  5. Prove that the area of triangle formed by the tangents to the parabola...

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  6. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

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  7. If P, Q, R are three points on a parabola y^2=4ax whose ordinates are ...

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  8. Prove that any three tangents to a parabola whose slopes are in harmon...

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  9. Two straight lines are perpendicular to each other. One of them touche...

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  10. Find the equation of the chord to the parabola y^2=4axwhose middle poi...

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  11. Prove that the normal chord to a parabola at the point whose ordinate ...

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  12. Show that the area formed by the normals to y^2=4ax at the points t1,t...

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  13. P & Q are the points of contact of the tangents drawn from the point T...

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  14. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

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  15. Find the centre and radius of the smaller of the two circles that touc...

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  16. Prove that the length of the intercept on the normal at the point P(a ...

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  17. Prove that the locus of the middle pointsof chords of the parabolay^2=...

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  18. Prove that the locus of a point, which moves so that its distance from...

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  19. 5. The locus of point of intersection of two tangents to the parabola ...

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  20. Find the locus of the intersection of normals to the parabolay^2=4axat...

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