# Equation of the circle

1. Find the equation of the circle with center at the intersection of 4x + y - 4 = 0 and x - y - 6 = 0 and passing through (-1, -3).

2. What is the equation of the circle passing through (12, 1) & (2, -3) and having its center on the line 2x - 5y + 10 = 0.

3. The sides of the triangle are on the lines 3x - y - 5 = 0, x + 3y - 1 = 0 and x - 3y + 7 = 0. Find the equation of the circle inscribed in the triangle.

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#### Solution Preview

1. Find the equation of the circle with center at the intersection of 4x + y - 4 = 0

and x - y - 6 = 0 and passing through (-1, -3)

Center is given to lie on both the lines 4x + y - 4 = 0 and x - y - 6 = 0

Adding the equations, we get 5x-10=0. This gives x=2. Substituting in the second equation, we get 2-y-4=0 ie y=-2

Hence the center is (2, -2). It is given that the circle passes through (-1, -3). Hence the radius is given by . Hence the equation to the circle is given by . In the standard form, it is given as

2. What is the equation of the circle ...

#### Solution Summary

Equation of the circle is exemplified.