Question

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

Answer 1

The standard form for a circle is
`(x-h) ^(2)+(y-k) ^(2) = r^(2)`. We have our h and k, and we also have x and y. So let's fill in accordingly and solve for the radius squared term.
`(-4-(-1)) ^(2) +(0-(-4)) ^(2)= r^(2)`. Simplifying we get
`9+16= r^(2)` or 25. Now let's rewrite the equation with the radius term:
`(x+1) ^(2)+(y+4) ^(2)=25`