Question

Find the length of the chord of the circle x² + y² − 10x − 20y − 44 = 0 on the line 3x − 4y = 0. 

Answer 1

C = (5, 10) is the centre and r = 13 is the radius of the given circle. Suppose the line 3x − 4y = 0 cuts the circle at points A and B and M is the midpoint of AB (see Fig.). Therefore, CM is the perpendicular drawn to AB which is given by

Aliter: Put y = 3x/4 in the equation of the circle so that we have

Hence, the points are A = (88/5, 66/5) and B = (−8/5, −6/5) and the length is given by