If A Line Passes Through Two Points (1, 5) And (3, 7) Find Its Equation.

If a² + b² – c² – 2ab = 0 then the point of concurrency of family of straight lines ax + by + c = 0lies on the line –

All chords of the curve 3x² – y² –2x + 4y = 0 that subtends a right angle at the origin, pass through a fixed point whose co-ordinate is –

In a triangle ABC,  and point A lies on line y = 2x + 3 where  Area of  is such that [∆] = 5. Possible co-ordinates of ∆ is/are –

 then the point (x, y) lies on same side of the line 2x + y – 6 = 0 as the point –

Find the area of the quadrilateral with vertices (3, 3), (1, 4), (–2, 1), (2, –3).

A straight line segment of length ‘p’ moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2.

Find the acute angle between the two lines with slopes 1/5 and 3/2.

If a line has a slope = ½ and passes through (–1, 2); find its equation. 

If a line has a slope 1/2 and cuts off along the positive y-axis of length 5/2 find the equation of the line.

A straight line passes through a point A (1, 2) and makes an angle 60^owith the x-axis. This line intersects the line x + y = 6 at the point P. find AP.