The foci of the ellipse are (0, - 4) and (0, 4), which are on the y - axis with c = 4.

The center of the ellipse is (0 + 02, - 4 + 42) = (0, 0).

Length of the semiminor axis is b = 82 = 4

a² = b² + c² = 16 + 16 = 32

So, the standard equation of the ellipse is y232+x216 = 1

Vertex of the parabola = (0, 0)

Equation of the directrix is y = - 7

Since, y = - 7 is perpendicular to x - axis, x - axis is the focal axis of the parabola.

p = 7

So, the equation of the parabola in the standard form is x² = 4py or x² = 4(7)y ⇒ x² = 28y.

The foci of the ellipse are (0, - 3) and (0, 3) which are on the y - axis with c = 3.

The center of the ellipse = (0 + 02, -3 + 32) = (0, 0).

Length of the semi minor axis is b = 62 = 3

a² = b² + c² = 9 + 9 = 18

So, the standard equation of the ellipse is x29+y218 = 1.

Foci of the ellipse are (6, - 7) and (8, - 7).

Since the y - coordinates of foci are same, the focal axis of the ellipse is parallel to x - axis.

Distance between the foci = 2c = (8 - 6)2+(- 7 + 7)2 = 2 and hence c = 1

End points of the major axis are (5, - 7) and (9, - 7).

Distance between (5, - 7) and (9, - 7) = 2a = (9 - 5)2 +(- 7 + 7)2 = 4

So, length of the semi major axis = a = 42 = 2

b² = a² - c² = 4 - 1 = 3

Center of the ellipse, (h, k) = (5 + 92, - 7 - 72 ) = (7, - 7)

So, the equation of the ellipse is (x - 7)24+(y + 7)23 = 1.

The equation of a parabola with focus (a, 0) and directrix x = - a is y² = 4ax.

y² = 4(6) x

y² = 24x

A parabola with focus (0, c) and directrix y = - c, equation is given by x² = 4cy.

Since c = 6 > 0, it open upwards.

x² = 4(6)y = 24y

So, the equation of parabola is x² = 24y and it open upwards.

The equation of a parabola in the standard form whose directrix is the line y = p and focus is the point (0, - p) is x² = - 4py.

The directrix is y = 9 and the focus is (0, - 9). So, p = 9.

The equation of the parabola in the standard form is x² = - 36y.

A parabola with focus (0, c) and directrix y = - c, equation is given by x² = 4cy.

Since c = 3 > 0, it open upwards.

x² = 4(3)y = 12y

So, the equation of parabola is x² = 12y and it open upwards.

Foci of the ellipse are (4, - 8) and (10, - 8).

Since the y - coordinates of foci are same, the focal axis of the ellipse is parallel to x - axis.

Distance between the foci = 2c = (10 - 4)2+(- 8 + 8)2 = 6 and hence c = 3.

End points of the major axis are (5, - 8) and (15, - 8).

Distance between (5, - 8) and (15, - 8) = 2a = (15 - 5)2+(- 8 + 8)2 = 10

So, the length of the semimajor axis is a = 102 = 5

b² = a² - c² = 25 - 9 = 16

Since the center of the ellipse is midpoint of its major axis, center of the ellipse is (h, k) = (5+152, - 8 - 82 ) = (10 , - 8).

So, the equation of the ellipse in the standard form is (x - h)2a2+(y - k)2b2 = 1 ⇒ (x - 10)225+(y + 8)216 = 1.