7. Conic Sections Flashcards
The set of all points in a plane the sum of whose distances from two fixed points is constant is a/an ______.
The two fixed points are called the ______.
The two midpoint of the line segment connecting the two fixed points is the ______.
ellipse
foci
center
Consider the following equation in standard form:
x^2/25 + y²/9 = 1
The value of a² is _____, so the x-intercepts are _____ and ______.
The graph passes through _____ and ______, which are the vertices.
The value of b² is _____, so the y-intercepts are _____ and _____.
The graph passes through _____ and ______.
25
–5
5
(–5, 0)
(5, 0)
9
–3
3
(0, –3)
(0, 3)
Consider the following equation in standard form:
x²/9 + y²/25 = 1.
The value of a² is _____, so the y-intercepts are _____ and ______.
The graph passes through _____ and ______, which are the vertices.
The value of b² is _____, so the x-intercepts are _____ and _____.
The graph passes through _____ and ______.
25
–5
5
(0, –5)
(0, 5)
9
–3
3
(–3, 0)
(3, 0)
Consider an ellipse centered at the origin whose major axis is vertical. The equation of this ellipse in standard form indicates that a² = 9 and b² = 4.
Thus c² = _____.
The foci are located at _____ and _____.
5
(0, –√5)
(0, √5)
The graph of (x + 1)²/25 + (y – 4)²/9 = 1 has its center at _____.
(–1, 4)
If the center of an ellipse is (3, –2), the major axis is horizontal and parallel to the x-axis, and the distance from the center of the ellipse to its vertices is a = 5 units, then the coordinates of the vertices are ____ and _____.
(–2, –2)
8, –2
If the foci of an ellipse are located at (-8, 6) and (10, 12), then the coordinates of the center of the ellipse are _____.
(1, 9)
In the equation 3(x² + 4x) + 4(y² – 2y) = 32, we complete the square on x by adding ____ within the first parentheses.
We complete the square on y by adding _____ within the second parentheses.
Thus, we must add _____ to the right side of the equation.
4
1
16
