Point of contact when line `y=mx+c` touches the hyperbola

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the range of c for which the line y=mx+ c touches the parabola y^(2)=8(x+2)

The coordinates of the point of contact of the straight line y=mx+c to the parabola y^(2)=4ax is

Locus of P such that the chord of contact of P with respect to y^(2)=4ax touches the hyperbola x^(2)-y^(2)=a^(2)

If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45 , then lambda =

If the line y=mx+c touches the parabola y^(2)=4a(x+a) , then