The locus of the intersection of the two lines and , for different values of , is a hyperbola. The eccentricity of the hyperbola is:

Explanation: Solution Concept: Two curves and cut/touch at a point if . The eccentricity ( ) of the hyperbola is given by: Calculation: Let the equations of the lines be: If and intersect at a point , then we must have: Multiplying the first expression by gives us: Substituting this in : It can be observed that: The locus of the point of intersection is: Comparing this with the general equation of a hyperbola and using the eccentricity formula: Correct Option: 3. (2)

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NIMCET 2014 — Mathematics PYQ

NIMCET | Mathematics | 2014

The locus of the intersection of the two lines $\sqrt{3}x - y = 4k\sqrt{3}$ and $k(\sqrt{3}x + y) = 4\sqrt{3}$ , for different values of $k$ , is a hyperbola. The eccentricity of the hyperbola is:

NIMCET 2014 — Mathematics PYQ

Choose the correct answer:

Explanation

Solution

Concept:

Calculation:

Explanation

Solution

Concept:

Calculation:

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