Question

If m is a variable, then prove that the locus of the point of intersection of the lines `x/3-y/2=m and x/3+y/2=1/m` is a hyperbola.
A. parabola
B. ellipse
C. hyperbola
D. none of these

Answer 1

The required locus is obtained by eliminating the variable `m` from the given equations of the lines.
Thus, we have
`((x)/(3)-(y)/(2))((x)/(3)+(y)/(2))=m((1)/(m))implies(x^(2))/(9)-(y^(2))/(4)=1`
This is clearly a hyperbola.