Question

The lenght of the chord is x+y-1=0 w.r.t circle x^2 + y^2 -6x-8y=0 is?

Answer 1

Answer:

Step-by-step explanation:

You can subtract the equation of the 2nd circle from that of the 1st one, and that gives you a linear equation for the common cord. Rewrite both circle equations in the "standard" form so that you can find the centres of both circles. From that, you can compute the distance from one of the centres to the common cord (Distance from a point to a line) and proceed with possibly Pythagoras Theorem to get the common cord length.

This method, I suppose, circumvents the need of finding the two intersection points and lots of algebra involved.