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

The equations of the tangents to the hyperbola 9x²-16y² =144 at the ends of latus recta are

The locus of poles of  chords of the parabola  y²=4px which touch the hyperbola x²/a²-y²/b²=1is

If the equation of the hyperbola whose focus is (2, 4), eccentricity is 5 and directrix is 4x-3y+1=0 is 15x²-24xy+8y²+ax+by+c=0 then the ascending order of a, b, c is

The locus of  the point of intersection of two tangents of the hyperbola x²/a²+y²/b²=1 which  make an angle 30⁰ with one another is

A line through the origin meets the circle x²+y²=a² at P and the hyperbola x²-y²=a² at Q. The locus the point of  intersection of the tangent at P to the circle and with the tangent t Q to the hyperbola is

The equation to one asymptote of the hyperbola 14x²+38xy+20y²+x-7y-91=0 is 7x+5y-3=0, then the other asymptote is