. Foci ( , ± ), the conjugate axis is of length . . Foci ( ± , ), the latus rectum is of length .
. Foci ( ± , ), the latus rectum is of length . vertices ( ± , ), e = . .
Foci ( , ± ), passing through ( , ) Miscellaneous Examples Example The focus of a parabolic mirror as shown in Fig . is at a distance of cm from its vertex. If the mirror is cm deep, find the distance AB (Fig . ).
Solution Since the distance from the focus to the vertex is cm. We have, a = . If the origin is taken at the vertex and the axis of the mirror lies along the positive x -axis, the equation of the parabolic section is y = ( ) x = x Note that x = . Thus y = Therefore y = ± Hence AB = y = × = cm.
Example A beam is supported at its ends by supports which are metres apart. Since the load is concentrated at its centre, there CONIC SECTIONS is a deflection of cm at the centre and the deflected beam is in the shape of a parabola. How far from the centre is the deflection cm? Solution Let the vertex be at the lowest point and the axis vertical.
Let the coordinate axis be chosen as shown in Fig . . Fig . The equation of the parabola takes the form x = ay .
Since it passes through , , we have ( ) = a , i.e., a = × = m Let AB be the deflection of the beam which is