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 L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

Find the equation of a line passing through the point of intersection of the lines 4x+7y-3=0 and 2x-3y+1=0 that has equal intercepts on the axes.

Find the equation of a line perpendicular to the line x - 2y + 3 = 0 and passing through the point (1, -2) .

Find the equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x^2+y^2=9

From a point, P perpendicular PM and PN are drawn to x and y axes, respectively. If MN passes through fixed point (a,b), then locus of P is

Normal to the ellipse (x^2)/(64)+(y^2)/(49)=1 intersects the major and minor axes at Pa n dQ , respectively. Find the locus of the point dividing segment P Q in the ratio 2:1.

Find the equation of the lines passing through the point of intersection lines 4x-y+3=0 and 5x+2y+7=0 through the point (-1,2)

The line 6x+8y=48 intersects the coordinates axes at A and B, respecively. A line L bisects the area and the perimeter of triangle OAB, where O is the origin. The slope of line L can be