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

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 e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

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

The line lx+my=n is a normal to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1

Find the locus of the foot of perpendicular from the centre upon any normal to line hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 .

The line l x+m y+n=0 is a normal to the ellipse (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)

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

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2