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Two straight lines having variable slopes m 1 and m 2 pass through the fixed points a , 0 and - a , 0 respectively. If m 1 m 2 = 2 , then the eccentricity of the locus of the point of intersection of the lines is

Options

  1. A2
  2. B3
  3. C2
  4. D3 2

Correct answer

B. 3

Step-by-step solution

Let, the lines are y = m 1 x - a and y = m 2 x + a which intersects at the point h , k . ⇒ k = m 1 h - a & k = m 2 h + a ⇒ k 2 = m 1 m 2 h 2 - a 2 ⇒ k 2 2 = h 2 - a 2 (given, m 1 m 2 = 2 ) ⇒ x 2 1 - y 2 2 = a 2 (Hyperbola) Eccentricity = 1 + 2 1 = 3

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