Question

Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)

Answer 1

The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).

According to the question,

The circle with center at (-1,-4) that passes through the point (-4,0).

To find the radius of the circle:

Radius r = √[(-4 - (-1))² + (0- (-4))²]

=√(-4+1)² + (4)²

=√9+16

=√25

=5.

In order to find the standard equation of the circle is

(x - (-4))² + (y - (0))² = (5)²

(x + 4)² + (y )² = 25

x² + 8x + 16 + y² = 25

x² + y² + 8x + 16 = 25

x² + y² + 8x = 25 - 16

x² + y² + 8x = 9

x² + y² + 8x - 9 = 0

Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.

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