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Show that the locus of point of intersec...

Show that the locus of point of intersection of perpendicular tangents to the parabola `y(2)=4ax` is the directrix x+a=0.

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The correct Answer is:
Locus of `P` is `x+a=0`, which is the direcrix.
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Assertion (A) : The locus of the point of intersection of perpendicular tangents to y^(2) = 4ax is its directrix. Reason (R) : If theta is acute angle between the pair of tangents drawn from (x_(1),y_(2)) to parabola S =0 then tan theta= (sqrt(S_(11)))/(|x_(1)+a|) The correct answer is

AAKASH SERIES-PARABOLA-SOLVED EXAMPLES
  1. alpha and beta are the angles made by two tangents to the parabola y^(...

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  2. The normals from (P,0) are drawn to the parabola y^(2) = 8x, one of th...

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  3. Show that the locus of point of intersection of perpendicular tangents...

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  4. Show that the equation of the common tangent to the circle x^(2) + y^(...

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  5. The locus of the foot of the perpendicular from the focus to the tange...

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  6. Show that straight line 7x+6y=13 is a tangent to the parabola y^(2)-7x...

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  7. Find the condition for the line y=mx+c to be a tangent to the parabola...

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  8. If a chord of the parabola y^(2) = 4ax touches the parabola y^(2) = 4b...

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  9. Prove that two parabolas y(2)=4ax "and" x^(2)=4by intersect (other tha...

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  10. Show that the focal chord of the parabola y^(2)=4ax, which makes an an...

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  11. Show that semi latus rectum of the parabola y^(2) =4ax is the harmonic...

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  12. Prove that the locus of point of intersection of two perpendicular nor...

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  13. If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=...

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  14. Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to th...

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  15. Two parabolas have the same vertex and equal lengh of latus rectum su...

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  16. The sum of the ordinates of two points on y(2)=4ax is equal to the sum...

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  17. Prove that the portion of the tangent intercepted between the point of...

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  18. Prove that the radius of the circle whose centre is (-4,0) and which c...

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  19. A triangle ABC of area Delta is inserted in the parabola y^(2) =4ax su...

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  20. Prove that the circle on a focal radius of a parabola, as diameter tou...

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