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If a circle passes through the point (a,...

If a circle passes through the point `(a,b)` and cuts the circle `x ^(2) +y^(2) =p^(2)` orthogonally, then the equation of the locus of its centre is-

A

`x^(2) + y^(2) – 3ax – 4by + (a^(2) + b^(2) – p^(2)) = 0`

B

`2ax + 2by – (a^(2) – b^(2) + p^(2)) = 0`

C

`x^(2) + y^(2) – 2ax – 3by + (a^(2) – b^(2) – p^(2)) = 0`

D

`2ax + 2by – (a^(2) + b^(2) + p^(2)) = 0`

Text Solution

Verified by Experts

The correct Answer is:
D
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MOTION-CIRCLE-Exercise - 2(Level - I) (Objective Problems | JEE Main)
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  2. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  3. The chord of contact of tangents from three points P, Q, R to the circ...

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  4. If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

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  6. Find the equation of the pair of tangents drawn to the circle x^2 + y^...

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  7. If the circle x^2+y^2 +4x+22y + c = 0 bisects the circumference of the...

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  8. The lenght of the common chord of circles x^2+y^2-6x-16=0 and x^2+y^2-...

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  10. If two circles (x-1) ^(2) + (y-3) ^(2) =r^(2)and x ^(2) +y^(2) -8x +2y...

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  11. If the circles x ^(2) +y^(2) +2ax+cy+a=0 and x ^(2) +y^(2) -3ax+dy-1=0...

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  12. If a circle passes through the point (a,b) and cuts the circle x ^(2) ...

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  13. The equation of the circle which passes through (2a, 0) and has the ra...

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  14. Find the equation of the circle which cuts the three circles x^2+y^2-3...

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  15. A variable circle passes through the fixed point A(p,q) and touches t...

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  16. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  17. The common chord of two intersecting circdes C1, and C2 can be seen fr...

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  18. What is the length of the the shortest path by which one can go from (...

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  19. In a right triangle ABC, right angled at A, on the leg AC as diameter,...

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  20. A circle is inscribed ti.e. touches all four sides ) into a rhombous A...

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