Draw the shape o hyperbola `(x^(2))/(49) - (y^(2))/(9) = 1` and find the following :
(i) Centre, (ii) Transverse axis, (iii) conjugate axis, (iv) vetices, (v) eccentricity, (vi) foci, (vii) Directrices.

Draw the shape of ellipse (x^(2))/(16) +(y^(2))/(9) = 1 and find the following: (i) major axis, (ii) minor axis, (iii) vetices, (iv) eccentricity, (v) foci, (vi) Length of latus rectum.

Find the length of the transverse axis, conjugate axis, eccentricity, vertices, foci and directrices of the hyperbola 9x^2 - 16y^2 = 144 .

Find the equation of hyperbola with centre at origin, transverse axis along x axis, eccentricity sqrt(5) and sum of whose semi axis is 9.

For the hyperbola (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , the normal at point P meets the transverse axis AA' in G and the connjugate axis BB' in g and CF be perpendicular to the normal from the centre. Q. Locus of middle-point of G and g is a hyperbola of eccentricity

Show that the equation 7x^(2)-9y^(2)+54x-28y-116=0 represent a hyperbola. Find the coordinate of the centre, lenghts of transverse and conjugate axes, eccentricity, latusrectum, coordinates of foci, vertices and directrices of the hyperbola.

An ellipse passes through a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Foci of the ellipse are (A) (+- 4, 0) (B) (+-3, 0) (C) (+-5, 0) (D) none of these

Semi-conjugate axis of the hyperbola: 5y^(2) - 9x^(2) = 36 is

Find the length of the transverse and conjugate axes, eccentricity, centre, foci and directrices of the hyperbola. 9x^2 - 16y^2 - 72x + 96y - 144 = 0

In the hyperbola 4x^2 - 9y^2 = 36 , find the axes, the coordinates of the foci, the eccentricity, and the latus rectum.

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 4