Question

Relative to the circle with the equation x +y = 4, how has the circle with the equation (x + 5)2+(-6) = 4 been shifted?

What is the radius of the circle?

Answer 1

Circle (ii) shifted 5 units left and 6 units up to get the circle (iii).

The radius of the circle is 2 units.

Explanation:

The standard form of a circle is

`(x-h)^2+(y-k)^2=r^2` ...(i)

where, (h,k) is center and r is radius of the circle.

Consider the given equations of the circle are

`x+y=4` ...(ii)

`(x+5)^2+(x-6)^2=4` ...(iii)

From (i) and (ii), we get

`h=0,k=0,r^2=4\Rightarrow r=2`

So, the center of circle (ii) is (0,0) and radius is 2.

From (i) and (iii), we get

`h=-5,k=6,r^2=4\Rightarrow r=2`

So, the center of circle (iii) is (-5,6) and radius is 2.

Therefore, the circle (ii) shifted 5 units left and 6 units up to get the circle (iii). The radius of the circle is 2 units.