Consider a `DeltaABC` whose sides `AB, BC and CA` are represented by the straight lines `2x + y=0, x + py =q and x -y= 3` respectively. The point P is `(2,3)`. If P is orthocentre,then find the value of (p+q) is

If the straight lines x+q=0 , y-2 =0 and 3x+ 2y+5=0 are concurrent, then the value of q is-

Consider a DeltaABC in which sides AB and AC are perpendicular to x-y-4=0 and 2x-y-5=0, repectively. Vertex A is (-2, 3) and the circumcenter of DeltaABC is (3/2, 5/2). The equation of the line in List I is of the form ax+by+c=0, where a,b,c in I. Match it with the corresponding value of c in list II and then choose the correct code. Codes : {:(a, b, c, d),(r, s, p, q),(s, r, q, p),(q, p, s, r),(r, p, s, q):}

A line intersects the straight lines 5x-y-4=0 and 3x-4y-4=0 at A and B , respectively. If a point P(1,5) on the line A B is such that A P: P B=2:1 (internally), find point Adot

Find the angle between the straight lines : px-qy+r=0and(p+q)y+(q-p)x+r=0

A rectangle PQRS has its side PQ paralle to the line y=mx and vertices P,Q and S are on the straight lines y=a, x=b and x=-b respectively. Find the locus of the vertex R.

Find the image of the point (-3,-1) with respect to the straight line 3y+2x+22=0 .

In DeltaABC a straight line parallel to BC intersects the sides AB and AC at the points P and Q respectively. If AP=QC , AB=12cm , AQ=2cm , then find the value of CQ .

The equations of the sides AB,BC and CA of the CA of the DeltaABC are 3x+4y+3=0,2x+y+1=0and2x+3y+1=0 respectively . Find the equation of its altitude through the vertex A.

Find the value of p so that the three lines 3x + y - 2 = 0, px + 2y - 3 = 0 " and " 2x - y - 3 = 0 may intersect at one point.

If x= 3p and y=(2p)/5+1 , then find the value of p for which x = 5y.