The line common to the given families of line `a(x` `+y+1)+b(2x-3y-8)=0` and `lambda(x-y-1)+mu` `(2x-y-1)=0` is : `x+y+1=0` `x+y-1=0` `x+y-1=0` None of these

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

If it is possible to draw a line which belongs to all the given family of lines y-2x+1+lambda_1(2y-x-1)=0,3y-x-6+lambda_2(y-3x+6)=0 , a x+y-2+lambda_3(6x+a y-a)=0 , then (a) a=4 (b) a=3 (c) a=-2 (d) a=2

The equation of the circle whose diameter is the common chord of the circles; x^2+y^2+3x+2y+1=0 and x^2+y^2+3x+4y+2=0 is: x^2+y^2+8x+10 y+2=0 x^2+y^2-5x+4y+7=0 2x^2+2y^2+6x+2y+1=0 None of these

Consider the family of line (x+y-1)+lamda(2x+3y-5)=0 and (3x+2y-4)+mu(x+2y-6)=0 Equation of a straight line that belongs to both the families is:

The equation of the bisector of the acute angle between the lines 2x-y+4=0 and x-2y=1 is (a) x-y+5=0 (b) x-y+1=0 (c) x-y=5 (d) none of these

The line 4y - 3x + lambda =0 touches the circle x^2 + y^2 - 4x - 8y - 5 = 0 then lambda=

The length of the common chord of the circles x^(2)+y^(2)-2x-1=0 and x^(2)+y^(2)+4y-1=0 , is

The orthocenter of the triangle formed by lines x + y = 1, 2x + 3y =6 and 4x -y +4 =0 lines in quadrant number

The number of circles that touches all the three lines x+y-1=0, x-y-1=0 and y+1=0 is

Find the angle between the following pairs of lines : (i) x+2y-1=0 and 2x-y+3=0 (ii) y=5x+1 and y=-3x+2