P is a point equidistant from two lines l and m intersecting at point A (see figure). Show that the line AP bisects the angle between them.

AB is a line - segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B (See Fig ). Show that the line PQ is the perpendicular bisector of AB.

A line L passing through the point (2, 1) intersects the curve 4x^2+y^2-x+4y-2=0 at the point Aa n dB . If the lines joining the origin and the points A ,B are such that the coordinate axes are the bisectors between them, then find the equation of line Ldot

A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of 4/sqrt(3) units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (a) (-2/(sqrt(3)),2) (b) (0,0) (c) (2/(sqrt(3)),2) (d) (0,4)

(2, 1) is the points of intersection of two lines

Prove that a line cannot intersect a circle at more two points .

A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at angle 2alpha is a constant. Prove that the locus of points is an ellipse

In a parallelogram OABC, vectors veca, vecb, vecc are, respectively, tehe position vectors of vertices A, B, C with reference to O as origin. A point E is taken on the side BC which divides it in the ratio 2 : 1 . Also, the line segment AE intersects the line bisecting the angle angle AOC internally at point P. If CP when extended meets AB in point F, then The position vector of point P is

Show that the equation 2x^2-xy-3y^2-6x+19y-20=0 represents a pair of intersecting lines. Show further that the angle between them is tan^(-1) (5) .