﻿ C1 and C2 are circles of unit radius with centres at (0, 0) and (1, 0) respectively. C3 is a circle of unit radius, passes through the centres of the circles C1 and C2 and have its centre above x-axis. Equation of the common tangent to C1 and C3 which does not pass through C2 is : Kaysons Education

# C1 and C2 are Circles Of Unit Radius With Centres At (0, 0) And (1, 0) Respectively. C3 is A Circle Of Unit Radius, Passes Through The Centres Of The Circles C1 and C2 and Have Its Centre Above x-axis. Equation Of The Common Tangent To C1 and C3 which Does Not Pass Through C2 is

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## Question

### Solution

Correct option is

Equation of any circle through (0, 0) and (1, 0) is

If it represents C3, its radius = 1

As the centre of C3, lies above the x-axis, we take  and thus an equation of C3 is  . Since C1 and C3 intersect and are of unit radius, their common tangents are parallel to the line joining their centres (0, 0) and

So, let the equation of a common tangent be

It will touch C1, if

From the figure, we observe that the required tangent makes positive intercept on the y-axis and negative on the x-axis and hence its equation is

#### SIMILAR QUESTIONS

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