Question

The circle x2+y2=36 is translated 5 Units left and 4 units up where is the center of the new circle after the translation

Answer 1

The general equation of a circle is given by:
(x-a)^2+(x-b)^2=r^2
where:
(a,b) is the center
r is the radius

given the equation:
x^2+y^2=36
it means that the equation is centered at (0,0) with radius of 6 units. Thus a translation of 5 units to the left and 4 units up, will change the new center to
(-5,4)
thus the equation will be:
(x+5)^2+(y-4)^2=36

Answer: (x+5)^2+(y-4)^2=36