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General Equation of Ellipse

71. Let C, C1...

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71. Let C, C1, C2 be circles of radii 5,3,2 respectively. C1 and C2 touch each other externally and C internally. A circle C3 touches C1 and C2 externally and C internally. If its radius is m/n, where m and n are relatively prime integers, then 2n-m is?

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Q. Three circles

C_{1}, C_{2}

C_{3}

r_{1}, r_{2}

r_{1} + r_{2}

respectively are such that

C_{1}

C_{2}

touch each other externally and

C_{3}

internally. Another circle with radius

r_{3}

touches all the three circles. If

r_{1} > r_{2} > r_{3}

r_{1}, r_{2}, r_{3}

are in A.P. then

{(\frac{r_{1}}{r_{2}})}^{3}

C_{1}

C_{2}

externally touch each other and they both internally touch another circle

C_{3}

C_{1}

C_{2}

4

10

respectiveley, and the centers of the three circles are collinear. A chord of

C_{3}

is a transverse common tangent to the circles

C_{1}

C_{2}

. Find the length of the chord

C_{1}, C_{2}

be two circles touching each other externally at the point A and let AB be the diameter of circle

C_{1}

. Draw a secant

B A_{3}

C_{2}

, intersecting circle

C_{1}

A_{1} (\neq A)

C_{2}

A_{2}

A_{3}

B A_{1} = 2

B A_{2} = 3

B A_{3} = 4

, then the radii of circles

C_{1}

C_{2}

are respectively.

C_{1}

C_{2}

are two non concentric fixed circle with radii

R_{1}

R_{2}

R_{2}

is contained in

C_{1}

. A third circle

C

moves in such a way that it touches

C_{1}

C_{2}

externally, then find the locus of its centre.

C_{1}

C_{2}

on Argand be given by

| z + 1 | = 3

| z - 2 | = 7

respectively. If a variable circle

| z - z_{0} | = r

be inside circle

C_{2}

such that it touches

C_{1}

C_{2}

internally then locus of '

Z_{0}

' describes a conic E whose eccentricity is equal to :

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