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If two circles and a(x^2 +y^2)+bx + cy =...

If two circles and `a(x^2 +y^2)+bx + cy =0` and `A(x^2+y^2)+Bx+Cy= 0` touch each other, then

A

aC=cA

B

bC=cB

C

aB=bA

D

a A=bB=cC

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly both are circles pass through the origin. The two circles will touch each other if they have a common tangent at the origin. The tangents at the origin to the two circles are bx+cy=0 and Bx+Cy=0. These two must be identical
`:. (b)/(B)=(c)/(C)rArr bC=Bc`
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OBJECTIVE RD SHARMA-CIRCLES-Section I - Solved Mcqs
  1. If the polar of a point (p,q) with respect to the circle x^2 +y^2=a^2 ...

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  2. The locus of the mid-points of the chords of the circle of lines radiÃ...

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  3. If two circles and a(x^2 +y^2)+bx + cy =0 and A(x^2+y^2)+Bx+Cy= 0 touc...

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  4. The circles x^(2)+y^(2)+2x-2y+1=0 and x^(2)+y^(2)-2x-2y+1=0 touch each...

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  5. The point of intersection of the common chords of three circles descri...

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  6. If P and Q are the points of intersection of the circles x^2+""y^2+...

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  7. If the chord of contact of tangents from a point P to a given circle p...

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  8. If one of the circles x^2+y^2+2ax+c=0 and x^2+y^2+2bx+c=0 lies within ...

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  9. The chord of contact of tangents from a point P to a circle passes thr...

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  10. The locus of the centre of circle which cuts off an intercept of const...

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  11. Let PQ and RS be tangents at the extremities of the diameter PR of a c...

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  12. A circle is given by x^2 + (y-1) ^2 = 1, another circle C touches it e...

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  13. A tangent to the circle x^(2)+y^(2)=1 through the point (0, 5) cuts t...

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  14. If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0...

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  15. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

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  16. If the common chord of the circles x^2 + (y - 2)^2 = 16 and x^2 + y^2 ...

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  17. Two circles are given such that they neither intersect nor touch. Then...

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  18. Let A B C D be a quadrilateral with are 18 , side A B parallel to the ...

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  19. The locus of the centre of a circle touching the circle x^2 + y^2 - 4y...

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  20. The equation of the locus of the middle point of a chord of the circle...

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