The line `l x+m y-n=0` is a normal to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` . then prove that `(a^2)/(l^2)-(b^2)/(m^2)=((a^2-b^2)^2)/(n^2)`

The line L x+m y+n=0 is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , if

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

If straight line lx + my + n=0 is a tangent of the ellipse x^2/a^2+y^2/b^2 = 1, then prove that a^2 l^2+ b^2 m^2 = n^2.

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x^(0), y^(0)).

If the pair of straight lines Ax^(2)+2Hxy+By^(2)=0 be conjugate diameters of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then prove that Aa^(2)=Bb^(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 .

If y=m x+c is a tangent to (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 then b^(2) =

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

The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

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