The tower of a bridge, hung in the form of a parabola have their tops $30$ meters above the roadway and are $200$ meters apart. If the cable is $5$ meters above the road way at the centre of the bridge, find the length of the vertical supporting cable from the centre.

Find the lengths of the principal axes, coordinates of the foci, equations of directrices, length of the latus rectum, distance between foci, and distance between directrices of the ellipse:

 $x^2/25+y^2/9=1$

Find the lengths of the principal axes, coordinates of the foci, equations of directrices, length of the latus rectum, the distance between foci, the distance between directrices of the ellipse:

$3x^2+4y^2=12$

Find the lengths of the principal axes, coordinates of the foci, equations of directrices, length of the latus rectum, the distance between foci, the distance between directrices of the ellipse:

$2x^2+6y^2=6$

Find the lengths of the principal axes, coordinates of the foci, equations of directrices, length of the latus rectum, the distance between foci, the distance between directrices of the ellipse:

$3x^2+4y^2=1.$

Find the equation of the ellipse in standard form if eccentricity$=\frac{3}{8}$ and distance between its foci$=6$.

Find the equation of the ellipse in standard form if the length of the major axis $10$ and the distance between foci is $8.$

Find the equation of the ellipse in standard form if distance between directrix is $18$ and eccentricity is $\frac{1}{3}.$