x^2=y^2-6x+8y=10
what shape is this?
Check the sign between X^2 and Y^2.maybe it should be a + sign:
X^2 + Y^2 - 6X + 8Y = 10.
Complete the squares:
X^2-6X+(-6/2)^2 + Y^2+8Y+(8/2)^2=10.
X^2-6X+9 + y^2+8Y+16 = 10+9+16 = 35,
(X-3)^2 + (Y+4)^2=35.The Eq of a circle
C(3,-4).
r = sqrt35 = 5.9.