Show that `3x^2-3y^2-18x+12y+2=0` represents a rectangular hyperbola. Find its centre, foci and eccentricity.

Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperbola.

Show that the equation 9 x^2-16 y^2-18 x+32 y-151=0 represents a hyperbola. Find the coordinates of the centre .

The length of the intercepts on the x and y-axes of a circle are 2a and 2b unit respectively. Prove that the locus of the centre of the circle is hyperbola whose equation x^2-y^2=a^2-b^2 . Translating the origin to a suitable point show that the equation 5x^2-4y^2-20x-8y-4=0 represents a hyperbola. Find its eccentricity, coordinates of foci and equations of the directrices.

Let 16 x^(2) - 3y^(2) - 32 x + 12 y = 44 represents a hyperbola . Then _

Show that the equation 9x^(2) - 16y^(2) - 18x - 64y - 199 = 0 represents the equation of a hyperbola, find the coordinates of its centre and foci and also the equations of its directrices

The equation 16 x^2-3y^2-32 x+12 y-44=0 represents a hyperbola. (a)the length of whose transvers axis is 4sqrt(3) (b)the length of whose conjugate is 4 (c)whose center is (-1,2) (d)whose eccentricity is sqrt((19)/3)

Suppose the circle having equation x^2+y^2=3 intersects the rectangular hyperbola x y=1 at points A ,B ,C ,a n dDdot The equation x^2+y^2-3+lambda(x y-1)=0,lambda in R , represents.

The foci of a hyperbola coincide with the foci of the ellipse x^2/25 +y^2/9 =1 . Find the equation of the hyperbola if its eccentricity is 2.

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

The eccentricity of the hyperbola x^2-y^2=4 is