If the circle x²+y²=a² intersects the hyperbola xy=c² in four points (x_i, y_i), for i=1,2,3 and 4 then y₁+y₂+y₃+y₄=

The equation of the normal at the positive end of the latus rectum of the hyperbola x²-3y²=144 is

The curve represented by x=a(cosh θ+sinh θ), y=b(cosh θ-sinh θ) is

The equation to hyperbola whose centre is (0,0) distance between the foci is 18 and between the directrices is 8 is

The locus of poles of tangents to the circle x²+y²=a²-b² w. r. t the hyperbola x²/a²-y²/b²=1is

If α and β are two points on the hyperbola x²/a²-y²/b²=1 and the chord joining these two points passes through the focus (ae, 0) then e cos α-β/2=

The foot of the normal 3x+4y=7 to the hyperbola 4x²-3y²=1 is

If the asymptotes of the hyperbola 14x²+38xy+20y²+x-7y-91=0 are 7x+5y-3=0, ax+by+c=0 then the descending order of a, b, c is

If m₁, m₂ are slopes of the tangents to the hyperbola x²/25-y²/16=1 which pass through the point (6, 2) then

The asymptotes of a hyperbola are parallel to 2x + 3y = O and 3x+2y=0.  Its centre is at (1,  2) and it  passes through the point (5, 3).  Its equation is