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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` .

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
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  2. Find the equation of the circle passing through (1,0) and (0,1) and h...

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

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  4. Find the equation of the ellipse referred to its axes as the axes of c...

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  5. The equation of the hyperbola whose foci are (- 2, 0) and (2, 0) and e...

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  6. Find the equation of the diagonal through the origin of the quadrilate...

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  7. Show that all chords of the curve 3x^2 -y^2- 2x+ 4y= 0, which subtend ...

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  8. A line is such that its segment between the straight line 5x-y-4=0 and...

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  9. Straight lines : 3x + 4y = 5 and 4x- 3y = 15 intersect at the point A....

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  10. Find the locus of a point whose sum of the distances from the origin a...

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  11. Given vertices A (1, 1), B (4, -2) and C (5, 5) of a triangle, find th...

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  12. If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C1 of diam...

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  13. Let S =x^2 + y^2 + 2gx + 2fy +c = 0 be a gives circle. Find the locus ...

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  14. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle....

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  15. Let P(x1,y1) be a point and let ax + by +c =0 be a line. If L (h, k) i...

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  16. Let P(x1,y1) be a point and let ax + by +c =0 be a line. If L (h, k) i...

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  17. Let A be the centre of the circle x^2+y^2-2x-4y-20=0. If the tangents ...

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  18. Find the equation of the circle passing through the point (0, 0) and t...

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  19. Find the equation of the circle which touches the circle x^(2)+y^(2)-6...

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  20. Three circles touch one another externally. The tangents at their poin...

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