= Therefore, the equation of the parabola is x = − y , i.e., x = – y . EXERCISE . In each of the following Exercises to , find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. .
y = x . x = – y In each of the Exercises to , find the equation of the parabola that satisfies the given conditions: CONIC SECTIONS Fig . Fig . Fig .
We denote the length of the major axis by a , the length of the minor axis by b and the distance between the foci by c . Thus, the length of the semi major axis is a and semi-minor axis is b (Fig11. ). .
Focus ( , ); directrix x = – . Focus ( ,– ); directrix y = . Vertex ( , ); focus ( , ) . Vertex ( , ); focus (– , ) .
Vertex ( , ) passing through ( , ) and axis is along x -axis. . Vertex ( , ), passing through ( , ) and symmetric with respect to y -axis. .
Ellipse Definition 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 two fixed points are called the foci (plural of ‘ focus ’) of the ellipse (Fig11. ).