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 .

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

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.

Show that the equation 5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 represents an ellipse. Find the co-ordinates of it's center

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

Show that the equation 5x^(2) + 9y ^(2) - 10 x + 90 y + 185 = 0 represents an ellipse and find the equations of the directrices of this ellipse .

Show that the equation 5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 repesents an ellipse. Find eccentricity

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

Show that the equation 5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 repesents an ellipse. Find length of latus rectum

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

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