Write the equation of the circle with center (-1, -3) and (-7, -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 = (-1, -3) and (x , y) = (-7, -5)

Substituting the values in standard form of equation we get,

(-7 - (-1))² + (-5 - (-3))² = r²

(-6)² + (-2)² = r²

r² = 36 + 4

r = √40

Thus, the radius of the circle is √40 units.

The equation of a circle can be written as 

(x - (-1))² + (y - (-3))² = (√40)²

(x + 1)² + (y + 3)² = 40

Therefore, the equation of a circle is (x + 1)² + (y + 3)² = 40.

Write the equation of the circle with center (-1, -3) and (-7, -5) a point on the circle.

Summary:

The equation of the circle with center (-1, -3) and (-7, -5) a point on the circle is (x + 1)² + (y + 3)² = 40.