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Show that the locus of a point that divides a chord of slope `2` of the parabola `y^2 = 4x` internally in the ratio `1:2` is parabola. Find the vertex of this parabola.

A

`(y+8/9)^(2)=4/9(x-2/9)`

B

`(y-8/9)^(2)=4/9(x-2/3)`

C

`(y-8/9)^(2)=4/9(x+2/9)`

D

`(y+8/9)^(2)=4/9(x+2/9)`

Text Solution

Verified by Experts

The correct Answer is:
B
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FIITJEE-PARABOLA-ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL - I)
  1. A parabola y^(2)=4axandx^(2)=4by intersect at two points. A circle is ...

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  2. Consider a circle with its centre lying on the focus of the parabola, ...

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  3. Show that the locus of a point that divides a chord of slope 2 of the ...

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  4. All chords of the parabola y^(2)=4x which subtend right angle at the o...

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  5. A variable chord PQ of the parabola y=4x^(2) subtends a right angle at...

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  6. P & Q are the points of contact of the tangents drawn from the point T...

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  7. Point on the curve y^(2)=4(x-10) which is nearest to the line x + y = ...

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  8. Find the locus of midpoint of family of chords lamdax+y=5(lamda is par...

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  9. The equation of the common tangent touching the circle (x-3)^(2)+y^(2)...

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  10. The mirror image of the parabola y^2=4x in the tangent to the parab...

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  11. Find the coordinates of a point on the parabola y=x^2+7x+2 which is cl...

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  12. If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line...

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  13. Find the locus of midpoint of family of chords lamdax+y=5(lamda is par...

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  14. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

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  15. The parabola y^2 = 4x and the circle (x-6)^2 + y^2 = r^2 will have no...

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  16. The normal at the point P(ap^2, 2ap) meets the parabola y^2= 4ax again...

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  17. If one end of the diameter of a circle is (3, 4) which touches the x-a...

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  18. The point on the parabola y^(2)=8x whose distance from the focus is 8 ...

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  19. Centre of locus of point of intersection of tangent to y^2 = 4ax, if t...

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  20. Two parabolas y^(2)=4a(x-lamda(1))andx^(2)=4a(y-lamda(2)) always touch...

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