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Parabola y^2=4a(x-c1) and x^2=4a(y-c2) w...

Parabola `y^2=4a(x-c_1) and x^2=4a(y-c_2)` where `c_1 and c_2` are variables, touch each other. Locus of their point of contact is

A

`xy=2a^(2)`

B

`xy=4a^(2)`

C

`xy=a^(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2) Let P(x,y) be the point of contact. At P, both of them must have the same slope. We have
`2y(dy)/(dx)=4a,2x=4a(dy)/(dx)`
Eliminating `dy//dx`, we get `xy=4a^(2)`.
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CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
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  2. The area of the triangle formed by the tangent and the normal to the ...

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  3. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) where c1 and c2 are variables, ...

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  4. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

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

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  6. The center of the circle which cuts parabola orthogonally the parabol...

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  7. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

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

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  9. find the equation of hyperabola where foci are (0,12) and (0,-12)and t...

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

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

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

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

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

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

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

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  17. The point of intersection of the tangents of the parabola y^2=4x drawn...

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  18. The angle between tangents to the parabola y^2=4ax at the points where...

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

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

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