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

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 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:

The line 5 x+12 y=9 touch the hyperbola x^(2)-9 y^(2)=9 at

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)

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

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 distance between the foci and the distance between the directrices of the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 are in the ratio 3 : 2 then a : b is

If the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (5)/(4) and 2x+3y-6=0 is a focal chord of the hyperbola, then the length of transverse axis is equal to _________

If the ecentricity of the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 is 5/4 and 2x+3y - 6 = 0 is focal chord of the hyperbola , then the length of tranverse axis is equal to _______.

Let P(6,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at the point P intersect the x -axis at (9,0) then the eccentricity of the hyperbola is