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The locus of the center of a circle whic...

The locus of the center of a circle which cuts orthogonally the parabola `y^2=4x` at (1,2) is a curve

A

(3,4)

B

(4,3)

C

(5,3)

D

(2,4)

Text Solution

Verified by Experts

The correct Answer is:
A
(1)
Tangent to the parabola `y^(2)=4x` at (1,2) will be the locus, i.e.,
2y=2(x+1)
or y=x+1
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CENGAGE-PARABOLA-Exercise (Single)
  1. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

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  2. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to

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  3. The locus of the center of a circle which cuts orthogonally the parabo...

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  4. If the parabola y=a x^2-6x+b passes through (0,2) and has its tangent ...

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  5. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

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  6. The tangent to y^(2)=ax make angles theta(1)andtheta(2) with the x-axi...

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  7. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

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  8. The straight lines joining any point P on the parabola y^2=4a x to the...

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  9. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

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  10. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

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  11. If the locus of the middle of point of contact of tangent drawn to the...

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  12. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

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  13. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

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  14. The point of intersection of the tangents of the parabola y^(2)=4x dra...

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  15. The angle between the tangents to the parabola y^2=4a x at the points ...

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  16. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

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  17. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0 ...

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  18. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  19. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  20. Radius of the circle that passes through the origin and touches the ...

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