Find the equation of the hyperbola in the form `x^2/a^2-y^2/b^2=1` given that : the distance between foci is 10 and `LR=9/2`

Find the equation of the hyperbola in the form x^2/a^2-y^2/b^2=1 given that : distance between the foci is 12 and e=3

Find the equation of the hyperbola in the form x^2/a^2-y^2/b^2=1 given that : transverse axis is 8 and e=3

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : distance between the foci is 10 and distance between the directrices is 12.

Find the equation of the hyperbola in the form x^2/a^2-y^2/b^2=1 given that : e=sqrt2 and equation of the directrix is x=2sqrt2

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : distance between the foci is 4 and distance between directrices is 20.

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : distance between the foci is 4 and distance between the directrices is 24.

Find the equation of the hyperbola in the form x^2/a^2-y^2/b^2=1 given that : length of conjugate axis is 8 and it passes through (5,1)

Find the equation of the hyperbola in the form x^2/a^2-y^2/b^2=1 given that : one vertex is (5,0) and the corresponding focus is (6,0) .

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : major axis is 10 and distance between foci is 8.

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : eccentricity is 1/4 and distance between foci is 4.