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.

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse.

Statement 1 : A bullet is fired and it hits a target. An observer in the same plane heard two sounds: the crack of the rifle and the thud of the bullet striking the target at the same instant. Then the locus of the observer is a hyperbola where the velocity of sound is smaller than the velocity of the bullet. Statement 2 : If the difference of distances of a point P from two fixed points is constant and less than the distance between the fixed points, then the locus of P is a hyperbola.

Given two points A and B. If area of triangle ABC is constant then locus of point C in space is

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c^2dot Find the equation to its locus.

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c dot Find the equation to its locus.

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

In triangle ABC, base BC is fixed. Then prove that the locus of vertex A such that tan B+tan C= Constant is parabola.

The sum of the squares of the distances of a moving point from two fixed points (a ,0)a n d(-a ,0) is equal to a constant quantity 2c^2dot Find the equation to its locus.

If A and B are two fixed points and P is a variable point such that PA + PB = 4 , the locus of P is

If the sum of the distances of a moving point from two fixed points (ae, 0) and (-ae, 0) be 2a , prove that the locus of the point is: x^2/a^2+ y^2/(a^2 (1-e^2) =1