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.

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.

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

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.

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

Find the locus of a point P that moves at a constant distant of two units from the X-axis

Find the locus of a point P that moves at a constant distant of three units from the Y-axis

Base BC of triangle ABC is fixed and opposite vertex A moves in such a way that tan.(B)/(2)tan.(C)/(2) is constant. Prove that locus of vertex A is ellipse.

Statement 1 : If aa n db are real numbers and c >0, then the locus represented by the equation |a y-b x|=csqrt((x-a)^2+(y-b)^2) is an ellipse. Statement 2 : An ellipse is the locus of a point which moves in a plane such that the ratio of its distances from a fixed point (i.e., focus) to that from the fixed line (i.e., directrix) is constant and less than 1.