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 = √[(x2 - x1)2 + (y2 - y1)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 = r2.

∴ Equation of the circle = (x - 3)2 + (y + 2)2 = 52

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 = 52.

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