If a normal of slope m to the parabola `y^2 = 4 a x` touches the hyperbola `x^2 - y^2 = a^2` , then

If a normal of slope m to the parabola y^(2)=4ax touches the hyperbola x^(2)-y^(2)=a^(2), then

The line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if

The line y=x+2 touches the hyperbola 5x^2-9y^2=45 at the point

A normal to the parabola y^(2)=4ax with slope m touches the rectangular hyperbola x^(2)-y^(2)=a^(2) if

If x+y=k is a normal to the parabola y^(2)=12x then it touches the parabola y^(2)=px then

A normal to the parabola y^(2)=4ax with slope m touches the rectangular hyperbola x^(2)-y^(2)=a^(2) if 1) m^(6)+4m^(4)-3m^(2)+1=0 2) m^(6)-4m^(4)+3m^(2)-1=0 3) m^(6)-4m^(4)-3m^(2)+1=0 4) none

Find the length of that focal chord of the parabola y^(2) = 4ax , which touches the rectangular hyperbola 2xy = a^(2) .

show that x-2y+1=0 touches the hyperbola x^(2)-6y^(2)=3