Straight LineHard
Question
Let L1 be a straight line passin through the origin and L2 be the straight line x + y = 1. If the ntercepts made by the circle x2 + y2 - x + 3y = 0 on L1 and L2 are equal, then which of the following equation can represent L1 ?
Options
A.x + y = 0
B.x - y = 0
C.x + 7 y = 0
D.x - 7 y = 0
Solution
Let equation of line L1 be y = mx. Intercepts made by L1 and L2 are at the same distance from the centre of the circle.
⇒ 8m2 + 8 = m2 + 6m + 9
⇒ 7m2 - 6m - 1 = 0
⇒ (7m + 1)(m - 1) = 0
⇒
, m = 1
Thus, two chords are x + 7 y = 0 and y - x = 0
Therefore, (b) and (c) are correct answers.
⇒ 8m2 + 8 = m2 + 6m + 9
⇒ 7m2 - 6m - 1 = 0
⇒ (7m + 1)(m - 1) = 0
⇒
, m = 1Thus, two chords are x + 7 y = 0 and y - x = 0
Therefore, (b) and (c) are correct answers.
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