CircleHard

Question

Two lines through (2, 3) from which the circle x2 + y2 = 25 intercepts chords of length 8 units have equations

Options

A. 2x + 3y = 13, x + 5y = 17
B. y = 3, 12x + 5y = 39

C. x = 2, 9x _ 11y = 51
D. none of these

Solution

Let slope of required line is m

y _ 3 = m(x _ 2)

Þ mx _ y +(3 _ 2m) = 0

length of ^ from origin

= 3

Þ 9 + 4m2 _ 12m = 9 + 9m2

Þ 5m2 + 12m = 0 Þ m = 0, _

Hence lines are y _ 3 = 0 Þ y = 3

y _ 3 = _(x _ 2) Þ 5y _ 15 = _12x + 24

Þ 12x + 5y = 39.

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