Conics

2018 December(B05) Math Question 10

13. A circle with the equation x2 + y2 = 144 is graphed in the standard (x,y) coordinate plane. At what points does the circle intersect the x-axis?

2021 June(D06) Math Question 13

25. Each side of a square is 4 cm long. One vertex of the square is at (6,2) on a square coordinate grid marked in centimeter units. Which of the following points on the grid could be another vertex of the square?

Equation of a Circle

2020 December(D03) Math Question 25

27. Graphed in the same standard (x,y) coordinate plane are a circle and a parabola. The circle has radius 3 and center (0,0). The parabola has vertex (-3,-2), has a vertical axis of symmetry, and passes through (-2,-1). The circle and the parabola intersect at how many

2015 June(73C) Math Question 27

2010 December(69A) Math Question 30

30. The circle in the standard (x,y) coordinate plane below has center (-8.5,7.5) and has radius 5 coordinate units. Which of the following is an equation of this circle?

2015 April(73G) Math Question 30

30. Which of the following is an equation of the circle in the standard (x,y) coordinate plane whose center is at (4,−3) and whose radius is 5 coordinate units long?

2021 December(E23) Math Question 30

The graph of x²/9 − y²/49 = 1 in the standard (x,y) coordinate plane has an x-intercept at which of the following points?

2025 October(J08) Math Question 31

2013 April(71G) Math Question 32

2019 December(C03) Math Question 33

2011 June(69F) Math Question 33

34. Which of the following intervals is the range of the functionf(x)=−(x−3)2 +4?

2021 June(D06) Math Question 34

34. In the standard (x,y) coordinate plane, a circle with its center at (8,5) and a radius of 9 coordinate units has which of the following equations?

2021 April(Z04) Math Question 34

2009 June(67C) Math Question 36

37. A parabola with equation y = ax2 is graphed in the standard (x,y) coordinate plane below. Point Z(p,q) lies on the parabola. For any point Z(p,q) on the parabola, which of the following points must also be on the parabola?

2013 June(71C) Math Question 37

39. Suppose that the parabola is rotated clockwise (c') by 90° about the origin. Which of the following :`,is an equation for the parabola that results. froni this rotation?

2013 June(71C) Math Question 39

2019 April(Z15) Math Question 40

2012 December(71A) Math Question 41

2011 April(67F) Math Question 41

42. Which of the following equations is that of a circle that
is in the standard (x,y) coordinate plane, has center
(1,--4), and has a radius of 5 coordinate units?

2019 June(B02) Math Question 42

2012 June(70C) Math Question 44

2011 June(69F) Math Question 45

45. Which of the following is an equation of a parabola that passes through the 3 points labeled in the standard (x,y) coordinate plane below?

2018 April(A09) Math Question 45

45. The function y = f(x) is graphed in the standard (x,y) coordinate plane below.

2017 December(A10) Math Question 45

2009 April(66F) Math Question 46

In the standard (x,y) coordinate plane, only 1 parabola of the form y = (x − h)² + k has x-intercepts of 3 and 15. Which of the following equations represents the axis of symmetry of this parabola?

2023 April(F11) Math Question 46

2020 June(C02) Math Question 47

2018 December(B05) Math Question 49

2012 December(71A) Math Question 49

51. Shown below in the standard (x,y) coordinate plane are 2 circles and 1 ellipse, each centered at (0,0). The larger circle has equation x2 + y2 = 25 and intersects the ellipse at exactly 2 points, both on the x-axis. The smaller circle has equation x2 + y2 = 4 and intersects the ellipse at exactly 2 points, both on the y-axis. Which of the following equations represents the ellipse?

2018 June(A11) Math Question 51

51. The ellipse shown in the standard (x,y) coordinate plane below has equation 93)2 + `-Y 255,2 = 1. Which of the

2018 April(A09) Math Question 51

51. The intersection of lines 1 and m forms the 4 angles LA, LB, LC, and LD. The measure of LB is 3f times the measure of LA. Which of the following values is closest to the measure of LA ?

2017 December(A10) Math Question 51

2010 April(68G) Math Question 52

52. In the standard (x,y) coordinate plane, the circle centered at (1,3) that passes through (4,7) is the set of all points that are:

2017 June(74C) Math Question 52

53. Graphed in the standard (x,y) coordinate plane below is an ellipse. The center of the ellipse is (0,0), and points (-5,0), (Q,3), (5,0), (0,-3), A(3,a), and B(3 ,b) lie on the ellipse. What is the distance, in coordinate units, from A to B ?

2016 April(73E) Math Question 53

2019 December(C03) Math Question 53

55. One of the following equations represents the ellipse shown below in the standard (x,y) coordinate plane. Which one?

2021 June(D06) Math Question 55

2019 April(B04) Math Question 56

In the standard (x,y) coordinate plane, one of the following is an equation of the circle that can be inscribed in the ellipse 4x² + 9y² = 36. Which equation is that?

2023 April(F11) Math Question 56

2012 April(70G) Math Question 57

58. One of the following equations determines the graph in the standard (x,y) coordinate plane below. Which one?

2014 December(72G) Math Question 58

The graph of which of the equations below is a hyperbola with the same asymptotes as the graph of x²/9 − y²/4 = 1?

35 February(Z14) Math Question 58

59. The ellipse in the standard (x,y) coordinate plane below is the graph of ((x-5)2)/25 + (y-3)2)/9 = 1. Which of the following points are the foci of the ellipse?

Ellipse

2021 April(D05) Math Question 59

59. In the standard (x,y) coordinate plane below, the endpoints of the major and minor axes of the ellipse are labeled. Which of the following equations determines the ellipse?

2020 December(D03) Math Question 59

60. The circle with equation x2 + (y — 1)2 = 1 is graphed in the standard (x,y) coordinate plane below. Suppose the circle rolls along the positive x-axis for 2 rotations and then stops. Which of the following is an equation of the circle in its new position?

2016 December(74H) Math Question 60

60. A right circular cone is intersected by a plane that is not parallel to the base and does not intersect the base or vertex, ps shown in the figure below. One of the following figures shows the shape of the intersection. Which figure is it?

ConicsThere are 47 ACT math questions under Conics

Sub-topics

2018 December(B05) Math Question 10

2021 June(D06) Math Question 13