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

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 CP and CD are semi-conjugate diameters of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , then CP^(2) + CD^(2) =

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

If the pair of lines b^2x^2-a^2y^2=0 are inclined at an angle theta , then the eccentricity of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is

the equation of a diameter conjugate to a diameter y=(b)/(a)x of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

If the straight line lx+my+n=0 be a normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then by the application of calculus, prove that (a^2)/(l^2)-(b^2)/(m^2)=((a^2+b^2)^2)/(n^2) .

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

If the pair of straight lines xy - x - y +1=0 & the line ax+2y-3=0 are concurrent then a =

Show that the tangents at the ends of conjugate diameters of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 intersect on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 .