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Question

The locus of the point of intersection of the lines (3)kx+ky43=0 and 3xy4(3)k=0 is a conic, whose eccentricity is

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Solution

3kx+ky=43 ......(1)
3kxky=43k2.....(2)
Adding equation (1) and (2)
23kx=43(k2+1)
x=2(k+1k)....(3)
Substracting equation (1) and (2)
y=23(1kk)....(4)
By (3) and (4)
x24y212=4
x216y248=1 Hyperbola
e2=1+4816
e=2

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