Conic sections: parabola ellipse and hyperbola in standard forms - One Line Questions
1.
What are the coordinates of the vertices of the hyperbola x^2/a^2 - y^2/b^2 = 1? —
(±a, 0)
2.
What are the coordinates of the foci of the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b)? —
(±c, 0)
3.
For the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), the foci are located at: —
(±c, 0) where c^2 = a^2 - b^2
4.
For the hyperbola x^2/a^2 - y^2/b^2 = 1, the foci are located at: —
(±c, 0) where c^2 = a^2 + b^2
5.
The vertices of the hyperbola y^2/a^2 - x^2/b^2 = 1 are at: —
(0, ±a)
6.
For the parabola x^2 = 4ay, what are the coordinates of the focus? —
(0, a)
7.
The equation 4x^2 + 9y^2 - 8x + 36y - 4 = 0 represents an ellipse. What is its center? —
(1, -2)
8.
The equation x^2 - 4x + 2y + 6 = 0 represents a parabola. What is its vertex? —
(2, -1)
9.
The equation 9x^2 - 4y^2 - 36x + 8y - 4 = 0 represents a hyperbola. What is its center? —
(2, 1)
10.
For a parabola y^2 = 4ax, what are the coordinates of the focus? —
(a, 0)
11.
If the vertex of a parabola is at (h, k) and it opens upwards, what is its standard equation? —
(x-h)^2 = 4a(y-k)
12.
The standard equation of a hyperbola centered at (h, k) with transverse axis parallel to the x-axis is: —
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
13.
The standard equation of an ellipse centered at (h, k) with major axis parallel to the x-axis is: —
(x-h)^2/a^2 + (y-k)^2/b^2 = 1 (a > b)
14.
The standard equation of a parabola with vertex at (h, k) and opening to the left is: —
(y-k)^2 = -4a(x-h)
15.
For an ellipse, the eccentricity 'e' always satisfies which condition? —
0 < e < 1
16.
What is the length of the latus rectum of a parabola? —
4a
17.
In the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), what is the length of the major axis? —
2a
18.
In the hyperbola x^2/a^2 - y^2/b^2 = 1, what is the length of the transverse axis? —
2a
19.
For the same ellipse, what is the length of the minor axis? —
2b
20.
What is the length of the latus rectum for the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b)? —
2b^2/a
21.
What is the length of the latus rectum for the hyperbola x^2/a^2 - y^2/b^2 = 1? —
2b^2/a
22.
What is the latus rectum of the parabola x^2 = 4ay? —
4a
23.
What is the condition for the line y = mx + c to be tangent to the parabola y^2 = 4ax? —
c = a/m
24.
What is the relationship between a, b, and c (distance from center to focus) in an ellipse where a > b? —
c^2 = a^2 - b^2
25.
What is the relationship between a, b, and c (distance from center to focus) in a hyperbola? —
c^2 = a^2 + b^2
26.
What is the condition for the line y = mx + c to be tangent to the hyperbola x^2/a^2 - y^2/b^2 = 1? —
c^2 = a^2m^2 - b^2
27.
What is the condition for the line y = mx + c to be tangent to the ellipse x^2/a^2 + y^2/b^2 = 1? —
c^2 = a^2m^2 + b^2
28.
What is the eccentricity of an ellipse? —
e = c/a
29.
What is the eccentricity of a hyperbola? —
e = c/a
30.
For a hyperbola, the eccentricity 'e' always satisfies which condition? —
e > 1
31.
A conic section where the eccentricity 0 < e < 1 is called a: —
Ellipse
32.
A conic section where the eccentricity e > 1 is called a: —
Hyperbola
33.
A conic section where the eccentricity e = 1 is called a: —
Parabola
34.
The equation x^2 = -12y represents a parabola opening in which direction? —
Downwards
35.
The directrix of the parabola y^2 = 4ax is the line: —
x = -a
36.
What is the equation of the directrix for the parabola y^2 = 4ax? —
x = -a
37.
Which of the following equations represents a parabola? —
y^2 = 4ax
38.
Which of the following equations represents a hyperbola? —
x^2/a^2 - y^2/b^2 = 1
39.
What is the standard equation of a hyperbola centered at the origin with the transverse axis along the x-axis? —
x^2/a^2 - y^2/b^2 = 1
40.
What is the standard equation of an ellipse centered at the origin with the major axis along the x-axis? —
x^2/a^2 + y^2/b^2 = 1 (a > b)
41.
The standard equation of an ellipse centered at the origin with the major axis along the y-axis is: —
x^2/b^2 + y^2/a^2 = 1 (a > b)
42.
For the parabola y^2 = 4ax, the axis of symmetry is the: —
x-axis
43.
For the ellipse x^2/a^2 + y^2/b^2 = 1 (a > b), the major axis lies on the: —
x-axis
44.
For the hyperbola x^2/a^2 - y^2/b^2 = 1, the transverse axis lies on the: —
x-axis
45.
The equation of the directrix for the parabola x^2 = 4ay is: —
y = -a
46.
What are the equations of the asymptotes for the hyperbola x^2/a^2 - y^2/b^2 = 1? —
y = ±(b/a)x
47.
What is the standard equation of a parabola with its vertex at the origin and opening to the right? —
y^2 = 4ax
48.
Which of the following equations represents an ellipse? —
x^2/a^2 + y^2/b^2 = 1
49.
The equation y^2/a^2 - x^2/b^2 = 1 represents a hyperbola with the transverse axis along the: —
y-axis