Let ABCD be a rectangle and P be any point in its plane. Show that `PA^2+PC^2=PB^2+PD^2` using coordinate geometry.

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

O is any point inside a rectangle. Prove that OA^2+OC^2=OB^2+OD^2 .

Let ABC is be a fixed triangle and P be veriable point in the plane of triangle ABC. Suppose a,b,c are lengths of sides BC,CA,AB opposite to angles A,B,C, respectively. If a(PA)^(2) +b(PB)^(2)+c(PC)^(2) is minimum, then point P with respect to DeltaABC is

The circle A and B of a line segment of constant length c unit slides upon the fixex rectangular axes OX and OY. If P be a point on the plane such that OAPB is a rectangle, then show that locus of the foot of the perpendicular drawn from P to AB is x^(2//3)+ y^(2//3)=c^(2//3) .

O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB^(2) + OD^(2)

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

Let ABCD is a square with sides of unit lenghts . Points E and F are taken on sides AB and AD respectively so that AE =AF . Let P be a point inside the square ABCD. The value of (PA)^(2)-(PB)^(2)+(PC)^(2)-(PD)^(2) is equal to -

If P be any point on the plane lx+my+nz=p and Q be a point on the line OP such that OP.OQ=p^(2) , then find the locus of the point Q.

The points (3, -2) (-2, 8) and (0, 4) are three points in a plane. Show that these points are collinear.

If y=mx+c is the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at any point on it, show that c^(2)=a^(2)m^(2)+b^(2). Find the coordinates of the point of contact.