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?

Answer 1

Answer:

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

The radius of the circle is 2 units.

Step-by-step 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.