The fix point through which the line `x(a + 2b) + y(a + 3b) = a + b` always passes for all values of `a` and `b`, is-

If the line (x)/( a) + (y)/( b) = passes through the points (2, -3) and (4,-5) then ( a, b) is

Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the curve y=be^(-(x)/(a)) lies on Y-axis.

A parabola (P) touches the conic x^2+xy+y^2-2x-2y+1=0 at the points when it is cut by the line x+y+1=0. If (a,b) is the vertex of the parabola (P), then the value of |a-b| is

Find the coordinates of the point which divides the line segment joining the points (a + b, a - b) and (a - b, a + b) in the ratio 3 : 2 internally

Find the value of ‘b’ for which the points A(1, 2), B(-1, b) and C(-3, -4) are collinear .

The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ-plane at the point (0, (17)/(2), -(13)/(2)) . Then,

Angle between the lines (x)/( a) + (y)/( b) and (x)/(a) - (y)/( b) = 1 is ….....

Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A(2,-2) and B(3,7).

If the straight line y = mx +c passes through the points (2,4) and (-3,6) , find the values of m and c .

If P(9a - 2, -b) divides line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1. find the values of a and b.