Show that the eqaution `16x^2-3y^2-32x+12y-44=0` represents a hyperbola. Find the length of axes and eccentricity.

Show that the equation: 3x^2+3y^2+12x+18y-11=0 represents a circle.

The equation x^2 / (12-k) + y^2 /(8-k) = 1 represents a hyperbola if

Show that the equations x^2+y^2-6x+4y-36=0 represents a circle,Also find its centre and radius.

If ax^(2)-y^(2)+4x-y=0 represents a pair off lines then a=

The equation 6x^(2)-xy-12y^(2)-8x+29y-14=0 represents a pair of lines, then the angle between them is ..............?

Show that the line 3x-4y+10=0 is tangent to the hyperbola x^2-4y^2=20 . Also find the point of contact.

If ax^(2)+6xy+3y^(2)-10x+10y-6=0 represents a pair of perpendicular lines, then |a|=

For the hyperbola x^2/a^2-y^2/b^2=1 , the values of a and b, if the transverse axis is 8 and eccentricity 3, are: