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).`

Find the conditions for the lines Ax^(2)+2Hxy+By^(2)=0 to the conjugate diameter of (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 .

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

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 lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the X -axis,then

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

For the ellipse,(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 the equation of the diameter conjugate ax-by=0 is-

The pairs of straight lines ax^(2)-2hxy-ay^(2)=0 and hx^(2)-2axy-gy^(2)=0 are such that

If any line perpendicular to the transverse axis cuts the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and the conjugate hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 at points P and Q, respectively,then prove that normal at P and Q meet on the x-axis.

If the pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 intersect on the y-axis,then prove that 2fgh=bg^(2)+ch^(2)