Let the line `x-8y+k=0`, `k in l` meets the rectangular hyperbola xy=1 at the points whose abscissae are integers then the number of such lines is

If the normals at (x_(i),y_(i)) i=1,2,3,4 to the rectangular hyperbola xy=2 meet at the point (3,4) then

If the line y=mx+a meets the parabola x^(2)=4ay in 2 points whose abscissae are x_(1) and x_(2) such that x_(1)+x_(2)=0 then m=

A straight line touches the rectangular hyperbola 9x^(2)-9y^(2)=8 and the parabola y^(2)=32x. An equation of the line is

If the line x-3y+5+ k(x+y-3)=0 , is perpendicular to the line x+y=1 , and k .

if the line 4x+3y+1=0 meets the parabola y^(2)=8x then the mid point of the chord is

The triangle formed by the tangent to the parabola y=x^(2) at the point whose abscissa is k where kin[1, 2] the y-axis and the straight line y=k^(2) has greatest area if k is equal to

The line 2x+y=0 passes through the centre of a rectangular hyperbola,one of whose asymptotes is x-y=1. The equation of the other asymptotes is