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Let (x, y) be any point on the parabola `y^(2) = 4x`. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is

A

`x^(2)=y`

B

`y^(2)=2x`

C

`y^(2)=x`

D

`x^(2)=2y`

Text Solution

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The correct Answer is:
C
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MOTION-PARABOLA-EXERCISE - IV
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  4. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  5. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  6. The tangent and normal at P(t), for all real positive t, to the parabo...

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  7. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

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  8. Consider the parabola y^(2) = 8x. Let Delta(1) be the area of the tria...

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  9. Let (x, y) be any point on the parabola y^(2) = 4x. Let P be the point...

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  10. Let L be a normal to the parabola y^(2) = 4x. If L passes through the ...

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  11. Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the ...

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  12. Let PQ be a focal chord of the parabola y^(2) = 4ax. The tangents to t...

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  13. line L:y=mx+3 meets y–axis at E(0, 3) and the are of the parabola y^(2...

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  14. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

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  15. Let a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, ...

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  16. If st = 1, then the tangent at P and the normal at S to the parabola m...

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  17. Let P and Q be distinct points on the parabola y^(2) = 2x such that a ...

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  18. The circle C(1) : x^(2)+y6(2)=3, with cenre at O, intersects the parab...

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  19. Let P be the point on the parabola y^(2) = 4x which is at the shortest...

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