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 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 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 : 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 : one vertex is (5,0) and the corresponding focus is (6,0) .

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)

For the standard hyperbola x^2/a^2-y^2/b^2=1 ,

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : length of the LR is 5/2 and eccentricity is sqrt3/2

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : major axis is 8, minor axis is 1/2

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : major axis is 2sqrt5 , eccentricity is 1/sqrt2

Find the equation of the ellipse in the form x^2/a^2+y^2/b^2=1(a>b) , given : major axis is 16, minor axis is 12.