A point moves such that the sum of the square of its distances from two fixed straight lines intersecting at angle `2alpha` is a constant. Prove that the locus of points is an ellipse

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

A point moves such that the sum of the squares of its distances from the two sides of length ‘a’ of a rectangle is twice the sum of the squares of its distances from the other two sides of length b. The locus of the point can be:

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an (a)circle (b) straight line (c) ellipse (d) none of these

Find the number of point of intersection of two straight lines .

A straight line moves so that the product of the length of the perpendiculars on it from two fixed points is constant. Prove that the locus of the feet of the perpendiculars from each of these points upon the straight line is a unique circle.

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the coordinate axes is a constant. Show that the plane passes through a fixed point.

Find the locus of appoint which moves such that the sum of the squares of its distance from the points A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.

Find the locus of appoint which moves such that the sum of the squares of its distance from the points A(1,2,3),B(2,-3,5)a n dC(0,7,4)i s120.

Statement 1 : In a triangle A B C , if base B C is fixed and the perimeter of the triangle is constant, then vertex A moves on an ellipse. Statement 2 : If the sum of the distances of a point P from two fixed points is constant, then the locus of P is a real ellipse.

If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.