Two straingt lines pass through the fixed points `(pma,0)` and have slopes whose product is `Pgt0`. Show that the locus of the points of intersection of the lines is a hyperbola.

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.

A moving straight line always passes through a fixed point (alpha , beta) . Prove that the locus of the middle point of the portion of the line intercepted between the axes is (alpha)/(x)+(beta)/(y) = 2 .

A moving straight line always passes through a fixed point (alpha,beta) .Prove that the locus of the middile point of the portion of the line intercepted between the axes is alpha/x+beta/y=2

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

The line through the points (a, b) and (-a, -b) passes through the point

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is,

Let A(a,0) and B(b,0) be fixed distinct points on the x-axis, none of which coincides with the O(0,0) , and let C be a point on the y-axis. Let L be a line through the O(0,0) and perpendicular to the line AC. The locus of the point of intersection of the lines L and BC if C varies along is (provided c^2 +ab != 0 )

Find the slope of the line passing through the given two point (a, 0) and (0, b)

Two lines passing through the point (2, 3) intersects each other at an angle of 60^(@) . If slope of one line is 2, find equation of the other line.

If the straight line ax+y+6=0 passes through the point of intersection of the lines x+y+4=0 and 2x+3y+10=0 , find a.