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`

The line y=(3x)/4 meets the lines x-y=0 and 2x-y=0 at points Aa n dB , respectively. If P on the line y=(3x)/4 satisfies the condition P AdotP B=25 , then the number of possible coordinates of P is____

A line is such that its segment between the lines 5x - y + 4 = 0 " and " 3x + 4y - 4 = 0 is bisected at the point (1, 5) . Obtain its equation.

Find the equation of the line through the intersection of the lines 3x+2y +5 = 0 and 3x - 4y +6 = 0 and the point (1,1)

A line is a drawn from P(4,3) to meet the lines L_1 and l_2 given by 3x+4y+5=0 and 3x+4y+15=0 at points A and B respectively. From A , a line perpendicular to L is drawn meeting the line L_2 at A_1 Similarly, from point B_1 Thus a parallelogram AA_1 B B_1 is formed. Then the equation of L so that the area of the parallelogram AA_1 B B_1 is the least is (a) x-7y+17=0 (b) 7x+y+31=0 (c) x-7y-17=0 (d) x+7y-31=0

Find the equation of the line through the intersection of the lines 3x + 2y + 5 = 0 and 3x - 4y + 6 = 0 and the point (1,1)

Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line x - 3y + 4 = 0 .

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 the straight line through the intersection of 5x-6y=1 and 3x+2y+5=0 and perpendicular to the straight line 3x-5y+11=0

a variable line L is drawn trough O(0,0) to meet the lines L_1:y-x-10=0 and L_2:y-x-20=0 at point A&B respectively .A point P is taken on line L the (1) if 2/(OP)=1/(OA)+1/(OB) then locus of P is (2) if (OP)^2=(OA)*(OB) then locus of P is (3) if 1/(OP)^2=1/(OA)^2+1/(OB)^2 then locus of point P is: