Question 886102
The two given points are on the circle {{{x^2+y^2=5^2}}}.  You can find a or b and use some sense of knowing where the points are on the circle to decide where the maximum length of PQ would show.  a and b are the two y-coordinates.


{{{y^2=25-x^2}}}
{{{highlight_green(y=0+- sqrt(25-x^2))}}}, TWO DIFFERENT VALUES.
You should be able to finish this.


Note that the four points will form a rectangle, and what YOU want is the coordinates of either or both DIAGONALs.   (Use the Distance Formula to find the diagonal length.)