EXERCISE 5.2

EXERCISE . . Find the equation of the parabola in each of the cases given below: (i) focus ( , ) and directrix x = − . (ii) passes through ( , and symmetric about y -axis. (iii) vertex( , and focus( , (iv) end points of latus rectum( , and( , ) . . Find the equation of the ellipse in each of the cases given below: (i) foci ± , e (ii) foci , ± ) and end points of major axis are , ± ) . (iii) length of latus rectum , eccentricity = , centre ( , ) and major axis on x -axis. (iv) length of latus rectum , distance between foci , centre ( , ) and major axis as y - axis. . Find the equation of the hyperbola in each of the cases given below: (i) foci ± , eccentricity = . (ii) Centre ( , ) , one of the foci ( , ) and corresponding directrix x = . (iii) passing through , − ) and the transverse axis is along the x axis and of length units. S '(− , ) C ( , ) S ( , ) y' x' O Two Dimensional Analytical Geometry - II Axis Ellipse Circle Parabola Hyperbola Axis Axis E C ◄ ◄ ◄ ◄ ◄ ◄ . Find the vertex, focus, equation of directrix and length of the latus rectum of the following: (i) y (ii) x (iii) y (iv) x (v) y . Identify the type of conic and find centre, foci, vertices, and directrices of each of the following: (i) x (ii) x (iii) x (iv) y . Prove that the length of the latus rectum of the hyperbola x = is a . . Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis. . Identify the type of conic and find centre, foci, vertices, and directrices of each of the following : (i) x ) + ) = (ii) x ) + ) = (iii) x ) − ) = (iv) y ) − ) = (v) (vi)