Write the equation of the circle with center (-3, -2) and (4, 5) a point on the circle.

Solution:

The standard form of the equation of a circle is given by

(x - a)² + (y - b)² = r²

Where, a and b are the coordinates of the centre

r is the radius

Given, centre = (-3, -2) and (x,y) = (4, 5)

Substituting the values in standard form of equation we get,

(4 - (-3))² + (5 - (-2))² = r²

(4 + 3)² + (5 + 2)² = r²

(7)² + (7)² = r²

r² = 49+49

r = √98

Thus, the radius of the circle is √98 units.

The equation of a circle can be written as 

(x - (-3))² + (y - (-2))² = (√98)²

(x + 3)² + (y + 2)² = 98

Therefore, the equation of a circle is (x + 3)² + (y + 2)² = 98.

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Write the equation of the circle with center (-3, -2) and (4, 5) a point on the circle.

Summary:

The equation of the circle with center (-3, -2) and (4, 5) a point on the circle is (x + 3)² + (y + 2)² = 98.