AIgo NotesQuiz for:
Conic Sections - Circles, Semicircles, Ellipses, Hyperbolas, and Parabolas
Question 24
What is the length of the latus rectum of a parabola?
A.P
B.2P
C.4P
D.None of the above
Question 1
What is the standard form of the equation of a circle with radius R and center coordinates (H, K)?
A.x - h^2 + y - k^2 = R^2
B.x^2 - h^2 + y^2 - k^2 = R^2
C.x - h^2 + y^2 - k^2 = R^2
D.x^2 - h^2 + y - k^2 = R^2
Question 2
What is the eccentricity of a circle?
A.1
B.0
C.0.5
D.None of the above
Question 3
What is the area of a circle with radius R?
A.πR^2
B.2πR
C.πR
D.4πR
Question 4
What is the circumference of a circle with radius R?
A.2πR
B.πR^2
C.4πR
D.πR
Question 5
What is the domain of a circle with center (H, K) and radius R?
A.H - R, H + R
B.K - R, K + R
C.H - K, H + K
D.K - H, K + H
Question 6
What is the range of a circle with center (H, K) and radius R?
A.K - R, K + R
B.H - R, H + R
C.K - H, K + H
D.H - K, H + K
Question 7
What is the equation of the upper semicircle of a circle with center (H, K) and radius R?
A.y = √(R^2 - (x - h)^2) + k
B.y = -√(R^2 - (x - h)^2) + k
C.y = √(R^2 - (x - h)^2) - k
D.y = -√(R^2 - (x - h)^2) - k
Question 8
What is the equation of the right semicircle of a circle with center (H, K) and radius R?
A.x = √(R^2 - (y - k)^2) + h
B.x = -√(R^2 - (y - k)^2) + h
C.x = √(R^2 - (y - k)^2) - h
D.x = -√(R^2 - (y - k)^2) - h
Question 9
In an ellipse, what is the length of the major axis if a > b and the major axis is horizontal?
A.2a
B.2b
C.a + b
D.a - b
Question 10
In an ellipse, what is the length of the minor axis if a > b and the major axis is horizontal?
A.2a
B.2b
C.a + b
D.a - b
Question 11
What is the equation of an ellipse with a horizontal major axis and center (H, K)?
A.x^2/h^2 + y^2/k^2 = 1
B.x^2/a^2 + y^2/b^2 = 1
C.x^2/b^2 + y^2/a^2 = 1
D.x^2/a^2 - y^2/b^2 = 1
Question 12
What is the equation of an ellipse with a vertical major axis and center (H, K)?
A.x^2/a^2 + y^2/b^2 = 1
B.x^2/b^2 + y^2/a^2 = 1
C.x^2/a^2 - y^2/b^2 = 1
D.x^2/h^2 + y^2/k^2 = 1
Question 13
What is the eccentricity of an ellipse?
A.0
B.1
C.e < 1
D.e > 1
Question 14
What is the formula for the area of an ellipse?
A.πab
B.2πab
C.πa^2
D.πb^2
Question 15
What is the formula for the approximate circumference of an ellipse?
A.π(a + b)
B.2π(a + b)
C.π√(a^2 + b^2)
D.2π√(a^2 + b^2)
Question 16
What is the equation of a hyperbola with a horizontal transverse axis and center (H, K)?
A.x^2/a^2 - y^2/b^2 = 1
B.x^2/b^2 - y^2/a^2 = 1
C.y^2/a^2 - x^2/b^2 = 1
D.y^2/b^2 - x^2/a^2 = 1
Question 17
What is the equation of a hyperbola with a vertical transverse axis and center (H, K)?
A.x^2/a^2 - y^2/b^2 = 1
B.x^2/b^2 - y^2/a^2 = 1
C.y^2/a^2 - x^2/b^2 = 1
D.y^2/b^2 - x^2/a^2 = 1
Question 18
What is the eccentricity of a hyperbola?
A.0
B.1
C.e < 1
D.e > 1
Question 19
What is the equation of the asymptotes of a hyperbola with a horizontal transverse axis?
A.y = ±b/a * (x - h)
B.y = ±a/b * (x - h)
C.y = ±b/a * (h - x)
D.y = ±a/b * (h - x)
Question 20
What is the equation of the asymptotes of a hyperbola with a vertical transverse axis?
A.y = ±b/a * (x - h)
B.y = ±a/b * (x - h)
C.y = ±b/a * (h - x)
D.y = ±a/b * (h - x)
Question 21
What is the equation of a parabola that opens to the right and has vertex (H, K)?
A.y = k^2 = 4p(x - h)
B.x = k^2 = 4p(y - k)
C.y = k^2 = 4p(x + h)
D.x = k^2 = 4p(y + k)
Question 22
What is the equation of a parabola that opens upward and has vertex (H, K)?
A.y = k^2 = 4p(x - h)
B.x = k^2 = 4p(y - k)
C.y = k^2 = 4p(x + h)
D.x = k^2 = 4p(y + k)
Question 23
What is the distance between the vertex and the focus of a parabola?
A.P
B.2P
C.4P
D.None of the above
Question 24
What is the length of the latus rectum of a parabola?
A.P
B.2P
C.4P
D.None of the above
Question 1
What is the standard form of the equation of a circle with radius R and center coordinates (H, K)?
A.x - h^2 + y - k^2 = R^2
B.x^2 - h^2 + y^2 - k^2 = R^2
C.x - h^2 + y^2 - k^2 = R^2
D.x^2 - h^2 + y - k^2 = R^2