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The vertex of the parabola y^(2) =8x is ...

The vertex of the parabola `y^(2) =8x` is at the centre of a circle and the parabola cuts the circle of the ends of the latus rectum. Then the equation of the circle is

A

`x^(2)+y^(2)=4`

B

`x^(2)+y^(2)=20`

C

`x^(2)+y^(2)=80`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, centre of the circle is at the origin.
The coordinates of the end-points of the latusrectum are L (2, 4) and L'(2, -4).
`:." Radius"=OL=sqrt(2^(2)-4^(2))=sqrt(20)`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
  1. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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  2. about to only mathematics

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  3. The vertex of the parabola y^(2) =8x is at the centre of a circle and...

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  4. Let A, B and C be three points taken on the parabola y^(2)=4ax with co...

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  5. Let there be two parabolas with the same axis, focus of each being ext...

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  6. Let A and B be two points on y^(2)=4ax such that normals to the curve ...

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  7. The set of real values of 'a' for which at least one tangent to y^(2)=...

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  8. The locus of the mid-point of the line segment joining a point on the ...

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  9. The tangent and normal at the point p(18, 12) of the parabola y^(2)=8x...

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  10. Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) me...

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  11. The points of the intersection of the curves whose parametric equation...

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

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  13. The radical centre of the circles drawn on the focal chords of y^(2)=4...

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  14. For each parabola y=x^(2)+px+q, meeting coordinate axes at 3-distinct ...

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  15. Let A(x(1),y(1)) and B(x(2),y(2)) be two points on the parabola y^(2) ...

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

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  17. the shortest distance between the line y-x=1 and the curve x=y^(2) ...

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  18. about to only mathematics

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

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

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