Question

What conic section is defined by all points in a plane where the difference between the lengths of segments x and y remains constant?

Answer 1

There are four type of conic generated when a double napped cone is cut by a plane

1.Circle

2.Parabola

3.Ellipse

4.Hyperbola

Among these four, Hyperbola is the conic , ,all points in a plane where the difference between the lengths of segments x and y remains constant.

A point on Semi major Axis=(a,0),lying on the Hyperbola.

A point on Semi Minor axis =(0,b),not lying on the Hyperbola.

Take a point D lying on the hyperbola,and two points M and N not lying on the hyperbola.

DM-DN=2a(Length of major axis)

Answer 2

hyperbola

Explanation:

If the sum is constant, the figure is an ellipse.

If the difference is constant, you get a hyperbola.

If one length is constant, you get a circle.

If the length to a point is the same as the length to a line, you get a parabola.