Prove that the straight line `lx+my+n=0` touches the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` if `a^(2)l^(2)-b^(2)m^(2)=n^(2)`.

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

If the line lx+my +n=0 touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is

Show that the line lx + my = 1 will touch the ellipse (x ^(2))/( a ^(2)) + (y ^(2))/(b ^(2)) =1 if a ^(2) l ^(2) + b ^(2)m ^(2) = 1.

If the l x+ my=1 is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then shown that (a^(2))/(l^(2))-(b^(2))/(m^(2))=(a^(2)+b^(2))^(2)

If the lines lx+my+n=0 passes through the extremities of a pair of conjugate diameters of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , show that a^(2)l^(2)-b^(2)m^(2)=0 .

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

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)-(y^2)/(b^2)=1 , then p^2dot

Prove that the line lx+my+n=0 toches the circle (x-a)^(2)+(y-b)^(2)=r^(2) if (al+bm+n)^(2)=r^(2)(l^(2)+m^(2))

Prove that the straight line 5x + 12 y = 9 touches the hyperbola x ^(2) - 9 y ^(2) =9 and find the point of contact.