Straight Lines

In a triangle PQR, the co-ordinates of the points P and Q are (-2, 4) and (4, -2) respectively. If the equation of the perpendicular bisector of PR is 2x - y + 2 = 0, then the centre of the circumcircle of the ΔPQR is:

If the line, 2x – y + 3 = 0 is at a distance 1/√5 and 2/√5 from the lines 4x – 2y + α = 0 and 6x – 3y + β = 0, respectively, then the sum of all possible values of α and β is

Let PQ be a diameter of the circle x² + y² = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is.

If the perpendicular bisector of the line segment joining the points P(1,4) and Q(k, 3) has y-intercept equal to -4, then a value of k is:

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1). If ∠BAC = 90°, and ar(?ABC) = 5√5 sq. units, then the abscissa of the vertex C is:

A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1). If ∠BAC = 90°, and ar(?ABC) = 5√5 sq. units, then the abscissa of the vertex C is:

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines L₁: 2x + y + 6 = 0 and L₂: 4x + 2y - p = 0, p > 0, at the points A and B, respectively. If AB = 9/√2 and the foot of the perpendicular from the point A on the line L₂ is M, then AM/BM is equal to