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  • If a variable circle touches externally two given circles, then the locus of the centre of the variable circle isOption: 1 a straight line &nb

If a variable circle touches externally two given circles, then the locus of the centre of the variable circle is

Option: 1

a straight line
 


Option: 2

a parabola
 


Option: 3

an ellipse
 


Option: 4

a hyperbola


Answers (1)

best_answer

 Let the variable circle be (x-h)^2+(y-k)^2=r^2

 and given circles are(x-a)^2+(y-b)^2=r_1^2

and (x-c)^2+(y-d)^2=r_2^2
According to figure

\begin{aligned} & C P=r_1+r \\ & \text { and } C Q=r_2+r \end{aligned}

\\ \therefore \quad C Q-C P=r_2-r_1= constant.\\ \because P, Q \: are \: fixed\: ard\: C \: is \: variable\\ \therefore Locus\: of \: C \: is\: a\: hyperbola

Posted by

Shailly goel

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