If a parabolic reflector is 20 cm in diameter and 5 cm in diameter and 5 cm deep, then its focus is ____________

(a)

(0, 5)

(b)

(5, 0)

(c)

(10, 0)

(d)

(0, 10)

The eccentricity of the ellipse 9x²+ 5y² - 30y = 0 is __________

(a)

\(\frac13\)

(b)

\(\frac23\)

(c)

\(\frac34\)

(d)

none of these

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)

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

If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is __________

(a)

6x² + 10y² = 5

(b)

6x² + 10y² = 15

(c)

x² + 3y² = 10

(d)

none

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 equation 7x²- 6\(\sqrt { 3 } \) xy + 13y² - 4\(\sqrt { 3 } \) x - 4y - 12 = 0 represents ____________

(a)

parabola

(b)

ellipse

(c)

hyperbola

(d)

rectangular hyperbola

The distance between the foci of a hyperbola is 16 and e = \(\sqrt { 2 } \). Its equation is ____________

(a)

x² - y² = 32

(b)

y² - x² = 32

(c)

x² - y² = 16

(d)

y² - x² = 16

When the eccentricity of a ellipse becomes zero, then it becomes a __________

(a)

straight line

(b)

circle

(c)

point

(d)

parabola

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

(a)

x² + y² = 4

(b)

x² +y² = 9

(c)

x² +y² = 45

(d)

x² +y² = 14

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

The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is ____________

(a)

5

(b)

\(\sqrt{45}\)

(c)

10

(d)

\(\sqrt{50}\)

If (1, -3) is the centre of the circle x² + y² + ax + by + 9 = 0 its radius is _________

(a)

\(\sqrt{10}\)

(b)

1

(c)

5

(d)

\(\sqrt{19}\)

The area of the circle (x - 2)² + (y - k)² = 25 is _________

(a)

25ㅠ

(b)

5ㅠ

(c)

10ㅠ

(d)

25

The equation of tangent at (1, 2) to the circle x² + y² = 5 is __________

(a)

x + y = 3

(b)

x + 2y = 3

(c)

x- y = 5

(d)

x - 2y = 5

If y = 2x + c is a tangent to the circle x² + y² = 5, then c is __________

(a)

土5

(b)

土\(\sqrt5\)

(c)

土5\(\sqrt2\)

(d)

±2\(\sqrt5\)