1. Find the equation of the parabola in each of the cases given below:
(i) focus (4, 0) and directrix x = -4 .
(ii) passes through (2, -3) and symmetric about y -axis.
(iii) vertex (1, -2) and focus (4, -2) .
(iv) end points of latus rectum (4, -8) and (4,8) .
2. Find the equation of the ellipse in each of the cases given below:
(i) foci ( ±3, 0), e = 1/2.
(ii) foci (0, ±4) and end points of major axis are(0,±5) .
(iii) length of latus rectum 8, eccentricity = 3/5 and major axis on x -axis.
(iv) length of latus rectum 4 , distance between foci 4√2 and major axis as y - axis.
3. Find the equation of the hyperbola in each of the cases given below:
(i) foci ( ±2, 0) , eccentricity = 3/2 .
(ii) Centre (2,1) , one of the foci (8,1) and corresponding directrix x = 4 .
(iii) passing through(5, -2) and length of the transverse axis along x axis and of length 8 units.
4. Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
(i) y2 = 16x
(ii) x2 = 24 y
(iii) y2 = -8x
(iv) x2 − 2x + 8 y +17 = 0
(v) y2 - 4 y - 8x +12 = 0
5. Identify the type of conic and find centre, foci, vertices, and directrices of each of the following:
6. Prove that the length of the latus rectum of the hyperbola
7. 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.
8. Identify the type of conic and find centre, foci, vertices, and directrices of each of the following :