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The locus of the midpoint of the segment joining the focus to a moving point on the parabola `y^2=4a x` is another parabola with directrix `y=0` (b) `x=-a` `x=0` (d) none of these

A

x = 0

B

x = -a/2

C

x = -a

D

x = a/2

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A
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FIITJEE-PARABOLA-ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL - I)
  1. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

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

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

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

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

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

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

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  8. Tangent to the curve y=x^(2)+6 at a point P(1, 7) touches the circle x...

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  9. The locus of the midpoint of the segment joining the focus to a moving...

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  10. Parabolas (y-alpha)^(2)=4a(x-beta)and(y-alpha)^(2)=4a'(x-beta') will h...

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  11. If the normals at the end points of a variable chord PQ of the parabol...

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  12. If the chord of contact of tangents from a point P(h, k) to the circle...

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  13. The axis of a parabola is along the line y = x and the distance of its...

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  14. If normal are drawn from a point P(h , k) to the parabola y^2=4a x , t...

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  15. The equation of the line of the shortest distance between the parabola...

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  16. The exhaustive set of values of k for which tangents drawn from the po...

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  17. The locus of the point (sqrt(3h),sqrt(sqrt(3)k+2)) if it lies on the l...

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  18. In a parabola y^(2)=4ax, two points P and Q are taken such that the ta...

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  19. Statement - 1: The equation of common tangent to the parabola y^(2)=4x...

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  20. Statement - 1: The focal chord to the parabola y^(2)=8x of length 7 un...

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