# Write the standard form of the equation of the circle with the given characteristics?

Center: (3, -2), Solution Point: (-1, 1)

**Solution:**

Given, center: (3, -2) and solution Point: (-1, 1)

By solution point, it means that the circle passes through that point. Hence, the radius of the circle is the distance between (3, -2) and (-1, 1).

Distance formula is given by D = √[(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}]

∴ Radius of the circle = √[(-1 - 3)^{2} + (1 + 2)^{2}] = √[(-4)^{2} + (3)^{2}]

∴ Radius of the circle = √25 = 5

We have, equation of the circle centered ant (h, k) and radius ‘r’ as (x - h)^{2} + (y - k)^{2} = r^{2}.

∴ Equation of the circle = (x - 3)^{2} + (y + 2)^{2} = 5^{2}

## Write the standard form of the equation of the circle with the given characteristics?

**Summary:**

The standard form of the equation of the circle with center: (3, -2) and solution Point: (-1, 1) is (x - 3)^{2} + (y + 2)^{2} = 5^{2}.

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