Let A (-2,2)and B (2,-2) be two points AB subtends an angle of `45^@` at any points P in the plane in such a way that area of `Delta PAB` is 8 square unit, then number of possibe position(s) of P is

The straight line (x)/(4)+(y)/(3) =1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9) =1 at two points A and B, there is a point P on this ellipse such that the area of DeltaPAB is equal to 6(sqrt(2)-1) . Then the number of such points (P) is/are

If A(-6,-6) and B(-6,4) be two points that a point P on the line AB satisfies AP=2//9AB . find the point P

Let A B C D be a rectangle and P be any point in its plane. Show that A P^2+P C^2=P B^2+P D^2dot

Let A(2,3) and B(2,-4) be two points. If P lie on the x - axis , such that AP = (3)/(7)AB , Find the coordinate of P.

A(-2, 0) and B(2,0) are two fixed points and P 1s a point such that PA-PB = 2 Let S be the circle x^2 + y^2 = r^2 , then match the following. If r=2 , then the number of points P satisfying PA-PB = 2 and lying on x^2 +y^2=r^2 is

Aa n dB are two points in the xy-plane, which are 2sqrt(2) units distance apart and subtend an angle of 90^0 at the point C(1,2) on the line x-y+1=0 , which is larger than any angle subtended by the line segment A B at any other point on the line. Find the equation(s) of the circle through the points A ,Ba n dCdot

Find the coordinate of a point P on the line segment joinig A(1,2) and B(6,7) in such a way that AP = (2)/(5) AB.

Let A = (1,1,-1) and B = (0, 2,1) be two given points .Also, let P:x+y+z=0 be a plane. The equation of the line perpendicular to vec(AB) and lying completely in the plane 'P' is

If the coordiantes of two points A and B are (3,4) and (5, -2) respectively. Find the coordinates of any point P if PA = PB and area of DeltaPAB =10 sq. units.