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If A,B,C are 3 points on a parabola , De...

If A,B,C are 3 points on a parabola , `Delta _1 , Delta_2 ` are the areas of triangles is formed by the points A, B,C and the tangents at A, B, C . If ` Delta_1, Delta _2 ` are the roots of `px^(2) +qx +r=0 ` then condition is

A

`9q^(2) =2pr`

B

` 9pr= 2q^(2) `

C

` 9p^(2) = 2qr`

D

` 2p^(2) =9qr `

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The correct Answer is:
B
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AAKASH SERIES-REVISION EXERCISE -PARABOLA
  1. Assertion (A) : Orthocentre of the triangle formed by any three tangen...

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  2. Show that length of perpendecular from focus 'S' of the parabola y^(2)...

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  3. If A,B,C are 3 points on a parabola , Delta 1 , Delta2 are the areas...

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  4. Prove that the orthocentre of the triangle formed by any three tangent...

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  5. The tangent at 't' on the parabola y^(2) =4ax is parallel to a normal ...

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  6. The no. of normals drawn to (y-1) ^(2) =8 ( x+3) through (4,1 )

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  7. The normal at 'P' cuts the axis of the parabola y^(2) =4ax in G and S...

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  8. If two of the three feet of normals drawn from a point to the parabola...

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  9. The equation of a tangent to the parabola y^(2) =8x is y =x+2 . The po...

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  10. The locus of middle points of normal chords of the parabola y^(2) = 4...

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  11. If the normals at P and Q meet again on y^(2) =4ax at R then centro...

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  12. If the normal to y^(2) =4ax at t1 cuts the parabola again at t2 th...

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  13. Point of concurrence of the normals drawn at (2,8) , (128,64) , (162, ...

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  14. If ( x1, y1) , (x2, y2) ,(x3y3) are feet of the three normals drawn f...

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  15. If two normals drawn to the y^(2) =8x at ( 2,4) and (18, 12) intersec...

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  16. If the normals at P and Q meet again on the parabola y^(2) =4ax then ...

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  17. The shortest distance between the line y-x =1 and the curve x=y^2 is

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  18. If the parabola y^(2)=ax passes through (1, 2) then the equation of th...

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  19. A set of parallel chords of the parabola y^(2) =4ax have their mid-po...

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  20. If the angular bisectors of the coordinates axes cut the parabola y^(2...

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