Geometric Equations Questions

High School Geometry Practice - Common Core Standards


This quiz is designed in accordance with the following Common Core State (CCS) standards:

QuestionCommon Core Standard #
3G.GPE.3 +
5G.GPE.3 +
6G.GPE.3 +
indicates a modeling standard.
+ indicates a college and career ready standard.

All questions of this quiz illustrate the difficulty of the high school G.GPE standards required for all students, including the college and career ready students.

Question 1: In the coordinate system, what is the equation of circle C, if the points of coordinates
(-2a,0), (0,2b) and the origin are all situated on the circle?

Question 2: If the focus of a parabola is (3, 1) and the directrix is y = 0, find the equation of the parabola.

Question 3: What is the equation of the ellipse with foci at (-4,0) and (4,0) and the sum of its focal radii being 10?

Question 4: The radius of the circle defined by the equation (x - 3)2 + (y - 1)2 = 81 is .

Question 5: If a is a real nonzero number, determine the foci of the hyperbola:

Question 6: What is the equation of the ellipse with foci at (-13,0) and (13,0) and vertices at (-12,0) and (12,0)?

Question 7: In the figure below, the four congruent circles of radius r are positioned in the coordinate plane so:
a) C1 is tangent to C2, C3 and the y axis
a) C2 is tangent to C1 and C4
a) C3 is tangent to C1, C4 and the x and y axes
a) C4 is tangent to C2, C3 and the x axis

What is the equation of the circle C, if C is tangent to all four circles of radius r?

Question 8: If three of the vertices of a rectangle in the coordinate plane are (0,4), (-2,0) and (0,-1), what are the coordinates of the fourth vertex?

Questions 9 and 10: In the coordinate plane, line y = mx + n is perpendicular to line y = nx + m, where m and n are integer numbers. Find the values of m and n if point (2,-1) is on the y = mx + n line.

m = .
n = .

Question 11: Find the coordinates of point P that lies along the directed line segment from A(-1,3) to B(4,-7) and partitions the segment in the ratio 3 to 2.

Select the correct answer:

Question 12: The perimeter of triangle of coordinates (-1,2), (2,2) and (2,-2) is:

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