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Let L1 be a line through the origin and L2 be the line x + y = 1. The circle x² + y² - x + 3y = 0 cuts equal-length chords on L1 and L2. Find the equation(s) of L1.

1. y = x and y = -7x
2. y = x only
3. y = -7x only
4. y = 2x and y = -3x

Correct answer: y = x and y = -7x

Solution

Setting the perpendicular distance from the centre (1/2, -3/2) to a line y = mx (through origin) equal to its distance to x + y = 1 yields two slopes, giving L1: y = x and y = -7x.

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