Question

Identify the equation or coordinates of the following conic and its equation.
Identify the center of the circle 34 = (x - 4)2 + (y + 7)2
Coordinates are ( , )

Answer 1

When a circle is centered at 0,0 its equation is of the form:
\[r^2=x^2+y^2\]
where r is the radius of the circle. When you displace x or y by x-a or x-b you just move the circle to a place centered at (a,b)

Answer 2

can you give a quick example please, because I still don't quite understand

Answer 3

you want
\[34 = (x - 4)^2 + (y + 7)^2\] to look like
\[r^2=(x-h)^2+(y-k)^2\] so you can read the answer right off the equation
in
\[r^2=(x-h)^2+(y-k)^2\] the radius is \(r\) and the center is \((h,k)\)
write your equation as
\[34=(x-4)^2+(y-(-7))^2\] and read the answer directly from the equation

Answer 4

yes thx