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Let P be the point (1,0) and Q be a poin...

Let P be the point (1,0) and Q be a point on the locus `y^(2)=8x`. The locus of the midpoint of PQ is

A

`x^(2)-4y=2=0`

B

`x^(2)+4y+2-0`

C

`y^(2)+4x+2=0`

D

`y^(2)-4x+2=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Let R(h, k) be the mid-point of PQ and the coordintes at Q be `(alpha, beta)`. Then,
`(alpha+1)/2=h" and "(beta+0)/2=krArralpha=h-1" and "beta=2k`
Since `Q (alpha, beta)` lies on the parabola `y^(2)=8x.`
`:." "beta^(2) -8alpharArr4k^(2)=8(2h-1)rArrk^(2)=4k-2`
Hence, the locus of (h, k) is `y^(2)=4x-2`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Chapter Test
  1. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

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  2. If y=2x+k is a tangent to the curve x^(2)=4y, then k is equal to

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  3. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

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  4. The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

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  5. The two ends of latusrectum of a parabola are the points (3, 6) and (-...

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  6. Prove that the locus of the middle points of all chords of the parabol...

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  7. The focus of the parabola x^2-8x+2y+7=0 is

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  8. The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-...

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  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

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  10. At what point on the parabola y^2=4x the normal makes equal angle with...

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  11. Three normals to the parabola y^2= x are drawn through a point (C, O) ...

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  12. The normal chord of a parabola y^2= 4ax at the point P(x1, x1) subten...

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  13. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

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  14. The circles on the focal radii of a parabola as diameter touch: A) th...

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  15. If the normals from any point to the parabola y^2=4x cut the line x=2 ...

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  16. about to only mathematics

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  17. The equation of the tangent to the parabola y^(2)=8x which is perpendi...

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  18. the tangent drawn at any point P to the parabola y^2= 4ax meets the di...

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  19. about to only mathematics

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  20. The parabola y^(2)=4ax passes through the point (2,-6). Find the lengt...

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  21. A variable circle passes through the fixed point (2, 0) and touches y-...

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