Two straight lines pass through the fixed points `(+-a, 0)` and have slopes whose products is `pgt0` Show that the locus of the points of intersection of the lines is a hyperbola.

Equation of straight line passing through the points (2,0) and (0, -3) is

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

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

A straight line passes through a fixed point (6, 8). Find the locus of the foot of the perpendicular on it drawn from the origin is.

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

The line l_(1) passing through the point (1,1) and the l_(2), passes through the point (-1,1) If the difference of the slope of lines is 2. Find the locus of the point of intersection of the l_(1) and l_(2)

A straight line passes through a fixed point (6,8) : Find the locus of the foot of the perpendicular drawn to it from the origin O.