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 the pair of lines b^(2) x^(2)-a^(2) y^(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 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)

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 (x^(2)+y^(2))(a^(2)+b^(2))=(ax+by)^(2) , prove that x/a = y/b .

If the pair of lines ax^(2)+2 h x y+b y^(2)+2 g x+2 f y+c=0 intersect on y -axis then

If the slope of one of the lines gives by ax^(2)+2hxy+by^(2)=0 is 5 times the other, then

If one of the slopes of the pair of the lines ax^(2) + 2 hxy + by^(2) = 0 is n times the other , then