C 1- C 2 are two circles of radii a- b a - b touching both the coordinate axes and have their centres in the first quadrant- Then the true statements among the following areA- If C1- C2 touch each other then b-a-3-2 -2B- If C 1- C 2 are orthogonal then b - a -2-3C- If C 1- C 2 intersect in such a way that their common chord has maximum length then b - a -3D- If C 2- passes through centre of C 1 then b - a -2-2

The correct options are A If C_1, C_2 touch each other then b/a = 3+2 √(2) B If C_1, C_2 are orthogonal then b/a = 2 + √(3) C If C_1, C_2 intersect in such a ...

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Byju's Answer

Standard XII

Mathematics

Intercept Made by Circle on Axes

C 1, C 2 are ...

Question

$C_{1}, C_{2}$ are two circles of radii a, b (a < b) touching both the coordinate axes and have their centres in the first quadrant. Then the true statements among the following are

If $C_{1}, C_{2}$ touch each other then $\frac{b}{a} = 3 + 2 \sqrt{2}$

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If $C_{1}, C_{2}$ are orthogonal then $\frac{b}{a} = 2 + \sqrt{3}$

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If $C_{1}, C_{2}$ intersect in such a way that their common chord has maximum length then $\frac{b}{a} = 3$

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If $C_{2}$ , passes through centre of $C_{1}$ then $\frac{b}{a} = 2 + \sqrt{2}$

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Solution

The correct options are
A
If $C_{1}, C_{2}$ touch each other then $\frac{b}{a} = 3 + 2 \sqrt{2}$

B
If $C_{1}, C_{2}$ are orthogonal then $\frac{b}{a} = 2 + \sqrt{3}$

C
If $C_{1}, C_{2}$ intersect in such a way that their common chord has maximum length then $\frac{b}{a} = 3$

D
If $C_{2}$ , passes through centre of $C_{1}$ then $\frac{b}{a} = 2 + \sqrt{2}$

Equation of $C_{1}$ is $(x - a)^{2} + (y - a)^{2} = a^{2}$

Equation of $C_{2}$ is $(x - b)^{2} + (y - b)^{2} = b^{2}$

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C1, C2 are two circles of radii a, b (a < b) touching both the coordinate axes and have their centres in the first quadrant. Then the true statements among the following are

$C_{1}, C_{2}$ are two circles of radii a, b (a < b) touching both the coordinate axes and have their centres in the first quadrant. Then the true statements among the following are