A line segment of length (a+b) units moves on a plane in such a way that its end points always lie on the coordinates axes. Suppose that P is a point on the line segment it in the ratio a:b. Prove that the locus of P is an ellipse.

A line of length (a+b) unit moves in such a way that its ends are always on two fixed perpendicular striaght lines. Prove that the locus of a point on this line which divides it into of lenghts a unit and b unit is an ellipse.

A rod AB of length 15 cm rests in between two coordinate axes is such a way that the end point A lies on x-axis and end Point B lies on y-axis. A point P (x,y) is taken on the rod in such a way that AP=6cm . Show that the locus of P is an ellipse.

The coordinates of the mid -point of line -segment joining the points (a,-b) and (-a,b) are -

Let O be the vertex and Q be any point on the parabola x^2=8y . IF the point P divides the line segment OQ internally in the ratio 1:3 , then the locus of P is

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _

A point P is moving in a cartesian plane in such a way that the area of the rectangle formed by the lines through P parallel to the coordinate axes together with ccordinate axes is constant. Find the equation of the locus of P .

Find the coordinates of the points of trisection of the line segment joining the points A(2,-2) and B(-7, 4).

A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the locus of a point, which divides the line into two portions of lenghts a unit and b units, is an ellipse. State the situation when the locus will be a circle.

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) in the ratio 1:3. Then the locus of P is :

Find the coordinates of the point which divides the line segment joining the points (-1, 7) and (4, -3) in the ratio 2:3 .