Show that the locus of the point of intersection of the lines `(x)/(a)-(y)/(b) = m` and `m((x)/(a)+(y)/(b)) = 1`, m being a verible parameter is a hyperbola.

If t is veriable paramete, parameter, show that the locus of the point of intersection of the straight lines (tx)/(a)+(y)/(b)-t = 0 and (x)/(a) - (ty)/(b) + 1 = 0 represents an ellipse

The point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 lies on

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

The locus of the point of intersection of the straight lines (x)/(a) + (y)/(b) = k and (x) /(a) - (y)/(b) = 1/k where k is a non-zero real variable is given by

For the variable t , the locus of the points of intersection of lines x - 2y = t and x + 2y = (1)/(t) is _

The locus of the point of intersection of the straight lines (x)/(a)+(y)/(b)=K and (x)/(a)-(y)/(b)=(1)/(K) , where K is a non - zero real variable, is given by

The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) and my-x=sqrt(a^2+b^2m^2) is

A variable straight line passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 and intersects the axes at P and Q. Find the locus of midpoint of PQ.

A variable straight line through the point of intersection of the two lines (x)/(3)+(y)/(2)=1and(x)/(2)+(y)/(3)=1 meets the coordinate axes at A and B . Find the locus of the middle point of AB.

The locus of the point of intersection of the lines sqrt3 x- y-4sqrt3 t= 0 & sqrt3 tx +ty-4 sqrt3=0 (where t is a parameter) is a hyperbola whose eccentricity is: