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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) and (x,y) n 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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ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  2. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

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

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

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

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  6. Let S be the focus of the parabola y^2=8x and let PQ be the common cho...

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

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

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  9. The slope of the line touching the parabolas y^2=4x and x^2=-32y is

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

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

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

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  13. Let O be the vertex and Q be any point on the parabola,x^2=""8y . I...

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  14. ·If the normals of the parabola y^2=4x drawn at the end points of it...

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  15. Let the curve C be the mirror image of the parabola y^2 = 4x with resp...

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  16. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

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  17. Let P be the point on the parabola, y^2=8x which is at a minimum dis...

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  18. The circle C1 : x2 + y2 = 3, with centre at O, intersects the parabola...

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

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  20. The radius of a circle, having minimum area, which touches the curve y...

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