If (0, 4) and (0, 2) are the vertex and focus of a parabola then its equation is ___________

(a)

x² + 8y = 32

(b)

y² + 8x = 32

(c)

x² - 8y = 32

(d)

y² - 8x = 32

Equation of tangent at (-4, -4) on x² = -4y is _____________

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

The length of the latus rectum of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 } \) = 1 is __________

(a)

\(\frac { 98 }{ 6 } \)

(b)

\(\frac { 72 }{ 7 } \)

(c)

\(\frac { 72 }{ 14 } \)

(d)

\(\frac { 98 }{ 12 } \)

In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is ________

(a)

\(\frac { 4 }{ 5 } \)

(b)

\(\frac { 1 }{ \sqrt { 52 } } \)

(c)

\(\frac { 3 }{ 5 } \)

(d)

\(\frac { 1 }{ 2 } \)

The auxiliary circle of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 } \) = 1 is __________

(a)

x² + y² = 25

(b)

x² + y² = 16

(c)

x² + y² = 41

(d)

x² + y² = 5