Given two points A(2, -3) and B(4, 0), find the equations to the locus of a point P such that the area of the triangle PAB is always 4sq. Units.

Find the equation to the locus of a point which moves such that the sum of the squares of its distances from the points A(1, 0) and B(-1, 0) is 10.

A(-a, 0) and B(a, 0) are two fixed points. Show that the locus of a point P such that /_ APB = 90^@ is x^2 + y^2 = a^2 .

Find the equation to the locus of a point which moves in a plane such that its distance from the point (1, 2) is equal to its distance from the Y-axis.

Using determinant find the values of k so that the area of the triangle with vertices at the points (k,0),(4,0) and (0,2) is 4 sq units.

If the centroid of a triangle is (1,4) and two of its vertices are (4,-3) and (-9,7) then the area of the triangle is

If the distance between the points (a, 0) and (0, 4) be 5 units, find the values of a.

The lion segment joining the points P(2, 1) and Q (-4, a) is trisected at the point ( 0, 7/8 ). Find the value of a.

The distance between the points A(2,-3) and B(2,2) is a)2 units b)3 units c)4 units d)5 units