Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x²-3y²=6. Their equations are

If the axes are rotated through an angle of 45⁰ in the anticlockwise direction then the equation of rectangular hyperbola x²-y²=a² changes to

The equation of the hyperbola whose centre is (1,2), one focus is (6,2) and transverse axis 6 is

The equation of the director circle of x²/12-y²/8=1 is

x²-y²+5x+8y-4=0 represents

The centre of the hyperbola 9x²-16y²+72x-32y-16=0 is

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x²-3y²=6. Their equations are

The locus  of the  midpoint its of chords of the hyperbola x²/a²-y²/b²=1 which pass through the positive end of the transverse axis is

The locus  of the  midpoint its of chords of x²/a²-y²/b²=1 which pass through the focus (ae, 0) is

The point of contact of 5x+6y+1=0 to the hyperbola 2x²-3y² =2 is