Two lines through `(2, 3)` from which the circle `x^2+y^2 =25` intercepts chords of length `8` units have equations
(A) `2x+3y=13`, `x+5y=17`
(B) `y= 3`, `12x+5y=39`
(C) `x=2`, `9x -11y=51`
(D) `y=0`, `12x+5y=39`

Options

A. `y=3`
B. `12x+5y=39`
C. `x=2`
D. `9x-11y=51`

Answer

1,2

Explanation

Let the slope the required line be m.
`y-3= m (x-2)`
`implies mx -y + (3-2m) = 0`
Length of perpendicular from origin `=3`
`implies 9 +4m^(2)-12m = 9+9m^(2)`
`implies 5m^(2)+12m=0`
`implies m=0, - (12)/(5)`
Hence, lines are
`y-3=0` or `y=3`
and `y-3=- (12)/(5) (x-2)` or `12x+5y=39`