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The tangent and normal at the point p(18...

The tangent and normal at the point p(18, 12) of the parabola `y^(2)=8x` intersects the x-axis at the point A and B respectively. The equation of the circle through P, A and B is given by

A

`x^(2)+y^(2)+4x-540=0`

B

`x^(2)+y^(2)-6x-360=0`

C

`x^(2)+y^(2)-4x-396=0`

D

`x^(2)+y^(2)-2x-444=0`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that
`PS=AS=SB`
`rArr" S is the circumcentre of "DeltaPAB`.

`:." Equation of the required circle is "`
`(x-2)^(2)+(y-0)^(2)=(2-18)^(2)+(0-12)^(2)`
`rArr" "x^(2)+y^(2)-4x-396=0`
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Section I - Solved Mcqs
  1. The set of real values of 'a' for which at least one tangent to y^(2)=...

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

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

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

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

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

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

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

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

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

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

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  12. about to only mathematics

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

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

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

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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. about to only mathematics

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  18. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

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  19. Let P be the point on the parabola y^(2)4x which is at the shortest di...

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

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