Multiple choice

If 2x - 3y = 0 is the equation of the common chord of the circles x2 + y2 + 4x = 0 and x2 + y2 + 2λy = 0 , then the value of λ is

  1. 3

  2. 2

  3. 1

  4. 0
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A Correct answer
Explanation

The common chord is found by subtracting the two circle equations: (x^2 + y^2 + 4x) - (x^2 + y^2 + 2*lambda*y) = 0, which simplifies to 4x - 2*lambda*y = 0. Comparing with 2x - 3y = 0, we get 4/2 = 2*lambda/3, so lambda = 3.

AI explanation

The common chord of two intersecting circles is found by subtracting their equations, which gives 4x - 2(lambda)(y) = 0. This equation must represent the same line as the given common chord 2x - 3y = 0, so we compare the coefficients. Dividing the first equation by 2 yields 2x - (lambda)(y) = 0. Equating the y coefficients gives lambda = 3. The result is 3.

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