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

Given two points A(2, -3) and B(4, 0), find the equations to the locus of a point P such that the area of the triangle PAB is always 4sq. Units.

On two mutually perpendicular lines,two points A and B are taken such that A is a variable point and B is a fixed point.A equilateral triangle ABC is completed.If the locus of the point C is alpha x+beta y=b, then alpha^(2)+beta^(2) is

A & B are two points on sqrt3x+y+1=0 such that AB is 3 and area of triangle ABC is 9. If locus of C in xy-plane is a pair of two parallel lines, then distance between them is

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

A ( 1 , - 1) , B ( 5, 2 ) are two points. If a point P forms a triangle of area 5 sq. Unit with A, B then the locus of P is

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

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 : 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.

Two points A and B with co-ordinates (5, 3), (3, -2) are given. A point P moves so that the area of DeltaPAB is constant and equal to 9 square units. Find the equation to the locus of the point P.