Type the correct answer in each box.A circle is centered at the point (5, -4) and passes through the point (-3, 2).The equation of this circle is (x + ____)²+ y(_____)²=_____

Accepted Solution

Answer:[tex](x-5)^2+(y+4)^2=100[/tex]Step-by-step explanation:step 1Find the radius of the circlewe know thatThe distance between the center and any point that lie on the circle is equal to the radiuswe have the points(5,-4) and (-3,2)    the formula to calculate the distance between two points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex] substitute the values[tex]r=\sqrt{(2+4)^{2}+(-3-5)^{2}}[/tex] [tex]r=\sqrt{(6)^{2}+(-8)^{2}}[/tex] [tex]r=\sqrt{100}\ units[/tex] [tex]r=10\ units[/tex] step 2Find the equation of the circlewe know thatThe equation of a circle in standard form is equal to[tex](x-h)^2+(y-k)^2=r^2[/tex]where(h,k) is the centerr is the radiuswe have[tex](h,k)=(5,-4)\\r=10\ units[/tex]substitute[tex](x-5)^2+(y+4)^2=10^2[/tex][tex](x-5)^2+(y+4)^2=100[/tex]