Conic Sections - Ellipse

Find the equations of the tangents to the ellipse `x^2/16 + y^2/9` = 1, making equal intercepts on co-ordinate axes

Find the 

1. lengths of the principal axes. 
2. co-ordinates of the focii 
3. equations of directrices 
4. length of the latus rectum
5. distance between focii 
6. distance between directrices of the ellipse:

3x² + 4y² = 1

Find the equation of the tangent to the ellipse x² + 4y² = 9 which are parallel to the line 2x + 3y – 5 = 0.

P and Q are two points on the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 with eccentric angles θ₁ and θ₂. Find the equation of the locus of the point of intersection of the tangents at P and Q if θ₁ + θ₂ = `π/2`

Find the

1. lengths of the principal axes.
2. co-ordinates of the focii
3. equations of directrics
4. length of the latus rectum
5. distance between focii
6. distance between directrices of the ellipse:

3x² + 4y² = 12

Find the equation of the ellipse in standard form if eccentricity = `3/8` and distance between its foci = 6

Find the equation of the ellipse in standard form if the distance between directrix is 18 and eccentricity is `1/3`.

Find the equation of the ellipse in standard form if the minor axis is 16 and eccentricity is `1/3`.