Two straight lines having variable slopes m_1 and m_2 pass through the fixed points a,0 and -a,0 respectively. If m_1m_2=2, then the eccentricity of…

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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_1m_2=2, then the eccentricity of the locus of the point of intersection of the lines is

MARKS Content Team · Accepted Answer

Correct answer: (B) √3. Let, the lines are y=m_1x-a and y=m_2x+a which intersects at the point h,k. ⇒k=m_1h-a & k=m_2h+a ⇒k^2=m_1m_2h^2-a^2 ⇒(k^2)/2=h^2-a^2 (given, m_1m_2=2) ⇒(x^2)/1-(y^2)/2=a^2 (Hyperbola) Eccentricity =√(1+21)=√3

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

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More Hyperbola Questions

Two straight lines having variable slopes m1 and m2 pass through the fixed points a,0 and -a,0 respectively. If m1m2=2, then the eccentricity of the locus of the point of intersection of the lines is

Solution

More Hyperbola Questions

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