If line `3x-a y-1=0` is parallel to the line `(a+2)x-y+3=0` then find the value of `adot`

If the plane 2x-y+z=0 is parallel to the line (2x-1)/2=(2-y)/2 =(z+1)/a , then the value of a is

If the line x+y=a touches the parabola y=x-x^2, then find the value of adot

The line joining the points A(2,1),a n dB(3,2) is perpendicular to the line (a^2)x+(a+2)y+2=0. Find the values of adot

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

If x^2+y^2-2x+2a y+a+3=0 represents the real circle with nonzero radius, then find the values of adot

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

Find the equation of line passing through point (2,-5) which is (i) parallel to the line 3x + 2y - 4 = 0 (ii) perpendicular to the line 3x + 2y - 4 =0

Let L be the line belonging to the family of straight lines (a+2b) x+(a-3b)y+a-8b =0, a, b in R, which is the farthest from the point (2, 2). If L is concurrent with the lines x-2y+1=0 and 3x-4y+ lambda=0 , then the value of lambda is