Question

Write the equation of a circle in standard form with diameter stack A B with bar on top. Where A(7, 5) and B(-1, -1). For full credit, show your work.

Answer 1

ANSWER

${(x - 3)}^{2} + {(y - 2)}^{2} = 25$

EXPLANATION

The given circle has diameter A(7,5) and B(-1,-1).

The center of the circle is the midpoint of the diameter.

The midpoint is given by the formula:

$(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

We substitute the points to get

$(\frac{7+ - 1}{2} , \frac{5+ - 1}{2} )$

$(3 , 2 )$

The radius of the circle is calculated using the center and any point on the circle.

$r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} }$

$r = \sqrt{ {(3- - 1)}^{2} + {(2 - - 1)}^{2} }$

$r = \sqrt{16 + 9 }$

$r = \sqrt{25} = 5$

We substitute the center and the radius into the standard equation of the circle.

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

Substitute the values to get,

${(x - 3)}^{2} + {(y - 2)}^{2} = {5}^{2}$

${(x - 3)}^{2} + {(y - 2)}^{2} = 25$