Question

Please help me. If you help step-by-steps that would really help. In the diagram, a circle of radius 2 moves in the direction of the arrow. If a point P(4, 3) on the circle stopped at point Q, the equation of the circle is $x^2+y^2+4x-2y+1=0$, find the length of the PQ.

Answer 1

2 was missing in front of the √10. I fixed it enjoy. (Thanks for the like.)

The equation of the circle is $(x^2+4x+4)+(y^2-2y+1)=4+1-1$.

This simplifies into the equation of $(x+2)^2+(y-1)^2=2^2$, and the diagram is correct.

In the diagram, the circle is tangent to the line. This shows the radius of the circle is perpendicular.

Now let's find out length PQ. It is faster to use the geometrical approach here because there is a right triangle already. Refer to the attachment.

Nice diagram. Your diagram was so visible to me so I could use it for the attachment. Hope this helps.