Question

Find the equation of the circle concentric with x*+y*-4x+6y=1 and having radius 4 units.​

Answer 1

Answer:

The equation of circle with centre at (h,k) and radius 'r' is (x-h)²+(y-k)²=r²

Expanding, x²-2hx+h²+y²+k²-2yk=r²

x²+y²-2hx-2yk+h²+k²-r²=0

Compare the above equation with

x²+y²-4x+6y-1=0

-2h=-4

h=-4/-2

h=2

Also, -2k=6

k=6/(-2)

k=-3

So the center of circle is at (h,k)=(2,-3)

The circles are concentric if they have the same center but different radius as r=4

So the equation of circle is

(x-2)²+(y-(-3))²=4²

(x-2)²+(y+3)²=16

x²-2.2.x+2²+y²+2.3.y+3²-16=0

x²-4x+4+y²+6y+9–16=0

x²+y²-4x+6y-3=0