#"the standard form of the equation of a circle is"#
#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#
#"where "(a,b)" are the coordinates of the centre and r is"#
#"the radius"#
#(x-3)^2+(y+7)^2=16" is in standard form"#
#"with "a=3,b=-7" and "r=sqrt16=4#
#rArr"centre "=(3,-7)" and "r=4#
#color(blue)"to find the intercepts"#
#"let x = 0, in the equation for y-intercepts"#
#"let y = 0, in the equation for x-intercepts"#
#x=0to(0-3)^2+(y+7)^2=16#
#rArr9+(y+7)^2=16#
#rArr(y+7)^2=7#
#color(blue)"take the square root of both sides"#
#rArry+7=+-sqrt7#
#rArry=-7+sqrt7" or "y=-7-sqrt7#
#rArry~~ -4.35" or "y~~ -9.65#
#rArr"y-intercepts "(0,-4.35),(0,-9.65)#
#y=0to(x-3)^2+(0+7)^2=16#
#rArr(x-3)^2=16-49=-33#
#(x-3)^2=-33" has no solution"#
#rArr"circle does not intercept with the x-axis"#
graph{(x-3)^2+(y+7)^2-16=0 [-22.5, 22.5, -11.25, 11.25]}
