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`.

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.

If the points (p, q) and (q, p) are equidistant from the point (x, y). show that x = y.

let A(1,3) and B(2,7) be two points. point P divides the line segment joining the point A(-1,3) and B(9,8) such that 'AP/BP=k/1'. if P lies on the line x- y + 2=0 find the value of k.

Show that the roots of the equation x^2 -2px + p^2 - q^2 + 2qr-r^2 = 0 are rational.

Let A(3,-1) and B(8,9) be two points in what ratio does the line x-y-2 = 0 divide the line segment AB.?

x and y are two positive integers such that 2,x, y are in A.P. and x, y, 9 are in G.P. then show that -x= 4, y= 6.

If a , b , c , are rational and a + b + c= 0 . Show that the roots of the following equation are rational. (b + c)x^2 + (c + a)x + (a + b) = 0

PA and PB are two tangents drawn from an external point P at the points A and B on a circle C(0,r).Prove that OP_|_AB

If A and B are two events such that P(A nn B) = 0.2, P(A uu B) = 0.8, P ( vec A ) = 0.4, find P (B).