Straight Line a...

A person standing at the junction (crossing) of two straight paths represented by the equations x + y + 1 = 0 and x – y + 1 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in least time.The equation of the path that he should follow is

If a, b, c are in A.P. and x, y, z are in G.P., then the points (a, x), (b, y) and (c, z) are collinear if

Through the point (13, 31) a st. line is drawn to meet the axes of x and y at Q and S respectively. If the rectangle OQRS is completed, the co–ordinates of R satisfy the equation.

If the vertices A and B of a triangle ABC are given by (2, 5) and (4, – 11) and C moves along the line L₁ : 9x + 7y + 4= 0, the locus of the centroid of the triangle ABC is a st. line parallel to

The vertex O of an isosceles triangle OAB lies at the origin and the equation of the base AB is x – y + 1 = 0. If OA = OB = 6, the area of the triangle OAB is

Given the points A (0, a) and B (0, – a), the equation of the locus of point P (x, y) such that |AP – BP| = 6 is

The points A (0, 0), B (cosα , sinα ) and C (cosβ, sinβ) are the vertices of a right angled triangle if