Question

Two lines through \( (2,3) \) from which the circle \( x ^{2}+ y ^{2}=25 \) intercepts chords of length 8 units have equations

(1) \( 2 x+3 y=13, x+5 y=17 \) 

(2) \( y=3,12 x+5 y=39 \) 

(3) \( x=2,9 x-11 y=51 \) 

(4) none of these

Comments

Correct answer is:- (2) y = 3, 12x + 5y = 39 

Answer 1

The correct option is (2) y = 3,12x + 5y = 39

The length of the chord intercepted by the circle x² + y² = a² on the straight line

Here a = 5 and y = mx + c passes through (2, 3), therefore 3 = 2m + c  i.e. c = 3 − 2m.

Thus, the equations of the required lines are y = 3 and 12x + 5y = 39.