Answer:
The point at which center of the image circle located is (-2, -3) so second option is correct.
Step-by-step explanation:
Given equation of circle is:
[tex](x-3)^{2} + (y+4)^{2} = 9[/tex] (i)
The general equation of circle is mentioned below,
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex] (ii)
Here 'r' represents the radius of the circle and (h,k) shown the center of the circle.
By comparing equation (i) and equation (ii), we get
r^2 = 9
r = 3
[tex](x-3)^{2} = (x-h)^{2}[/tex]
[tex](x-3) = (x-h)[/tex]
[tex]h = 3[/tex]
[tex](y+4)^{2} = (y-k)^{2}[/tex]
[tex](y+4) = (y-k)[/tex]
[tex]k = -4[/tex]
So the center of given circle is (h,k) = (3,-4)
Also, the circle is translated 5 units left, that is towards the -x-axis. Therefore h = 3 - 5 = -2
Also, the circle is translated 1 unit up, that is towards the +y-axis. Therefore k = -4 + 1 = -3
Hence, the point at which center of the image circle located is (-2, -3) so second option is correct.
