A point `P` moves in such a way that the ratio of its distance from two coplanar points is always a fixed number `(!=1)` . Then, identify the locus of the point.

Find the locus of a point such that the sum of its distance from the points (2, 2) and (2,-2) is 6.

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.

The ratio of the distances of a moving point from the points (3,4) and (1,-2) is 2:3 , find the locus of the moving point.

A point moves so that its distance from the point (2,0) is always (1)/(3) of its distances from the line y=x-18 . If the locus of the points is a conic, then length of its latus rectum is

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

The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units . Find the equation of the locus of the moving point.

A pole has to be erected at a point on the boundary of a circular ground of diameter 20m in such a way that the difference of its distance form two diameterically opposite fixed gates P and Q on the boundary is 4 m. Is it possible to do so? If answer is yes at what distance from the two gates should the pole be erected?

The sum of the distance of a moving point from the points (4,0) and (-4,0) is always 10 units. Find the equation to the locus of the moving point.