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Prove that any three tangents to a parab...

Prove that any three tangents to a parabola whose slopes are in harmonic progression enclose a triangle of constant area.

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If P, Q, R are three points on a parabola y^2=4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on :

If P, Q, R are three points on a parabola y^2=4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on :

Find the equation of the tangent to the parabola y^2=8x having slope 2 and also find the point of contact.

Find the equation of the tangent to the parabola y^2=8x having slope 2 and also find the point of contact.

Prove that the orthocentre of the triangle formed by any three tangents to a parabola lies on the directrix of the parabola

Tangents are drawn to the parabola at three distinct points. Prove that these tangent lines always make a triangle and that the locus of the orthocentre of the triangle is the directrix of the parabola.

On the parabola y^2 = 4ax , three points E, F, G are taken so that their ordinates are in geometrical progression. Prove that the tangents at E and G intersect on the ordinate passing through F .

On the parabola y^2 = 4ax , three points E, F, G are taken so that their ordinates are in geometrical progression. Prove that the tangents at E and G intersect on the ordinate passing through F .

Prove that through any point, three normals can be drawn to a parabola and the algebraic sum of the ordinates of the three points is zero.

Tangents are drawn from a variable point P to the parabola y^2 = 4ax such that they form a triangle of constant area c^2 with the tangent at the vertex. Show that the locus of P is x^2 (y^2 - 4ax) = 4c^4a^2 .

ARIHANT MATHS ENGLISH-PARABOLA-Exercise For Session 2
  1. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

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  2. The set of points on the axis of the parabola y^2-4x-2y+5=0 from which...

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

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  4. prove that the locus of the point of intersection of the tangents at t...

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  5. Find the equation of the normal to the parabola y^2=4x which is para...

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  6. Find the equation of the normal to the parabola y^2=4x which is perp...

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  7. The ordinates of points P and Q on the parabola y^2=12x are in the rat...

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  8. The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on th...

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  9. Three normals are drawn from (2lamda,0) to the parabola y^2=4x .Show t...

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  10. If m1,m2 are the slopes of the two tangents that are drawn from (2,3) ...

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  11. Find the angle between the tangents drawn from the origin to the pa...

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  12. If (a , b) is the midpoint of a chord passing through the vertex of th...

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  13. The diameter of the parabola y^2=6x corresponding to the system of par...

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  14. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

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  15. for parabola x^2+y^2+2xy−6x−2y+3=0, the focus is.

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  16. Find the locus of the middle points of the chords of the parabola y^2=...

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  17. A ray of light moving parallel to the x-axis gets reflected form a ...

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  18. The locus of the point of intersection of the tangents to the parabola...

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  19. about to only mathematics

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  20. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

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