# Summary

- The set of all points in a plane which are equidistant from a fixed point is a plane.
- The equation of a circle with the radius "r" and centre (h, k) is (x - h)
^{2}+ (y - k)^{2}= r^{2} - A conic section is the locus of a point which moves such that its distance from a fixed point always bears a constant ratio to its distance from a fixed line all being in the same plane.
- Depending on the eccentricity e, the conics are classified as follows
- if e = 0, the conic formed is a circle;
- if e < 1, the conic formed is an ellipse;
- if e = 1, the conic formed is a parabola;
- if e > 1, the conic formed is a hyperbola.

- A parabola is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is always a constant equal to its distance from a fixed straight line in the same plane.
- The equation of a parabola with focus (a, 0) where a > 0 and directrix x = -a is y
^{2}= 4ax. - The latus rectum of a parabola is a chord passing through the focus and perpendicular to the axis. The length of the latus rectum of a parabola y
^{2}= 4ax is 4a. - An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant.
- The equation of an ellipse with foci on the x - axis is .
- The latus rectum of an ellipse is a chord passing through any of the foci and perpendicular to the major axis. The length of the latus rectum of an ellipse is .
- The hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.
- The equation of a hyperbola with foci on the x - axis is : .
- Latus rectum of a hyperbola is a chord passing through any of the foci and perpendicular to the transverse axis. Its length is .