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: $(x+1) ^{2}+(y+4) ^{2}=25$