Coordinate Geometry and Properties of Geometric Figures Quiz

Test your knowledge of coordinate geometry with these questions on circles, lines, parabolas, ellipses, and hyperbolas.

Practice Learn Test

What is the equation of a circle with center (3, -4) and radius 5?

(x - 3)^2 + (y + 4)^2 = 5^2

(x + 3)^2 + (y - 4)^2 = 5^2

(x - 3)^2 + (y + 4)^2 = 25

(x + 3)^2 + (y - 4)^2 = 25

What are the coordinates of the midpoint of the line segment joining points (2, -3) and (6, 5)?

(4, 1)

(3, 2)

(5, 1)

(4, 2)

What is the equation of the line perpendicular to y = 3x - 2 passing through the point (2, -1)?

y = -1/3x + 2/3

y = -3x + 8

y = 1/3x - 1/3

y = 3x - 8

What is the standard form equation of an ellipse centered at (h, k) with semi-major axis a and semi-minor axis b?

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1

((x-h)^2)/(b^2) + ((y-k)^2)/(a^2) = 1

((x-h)^2)/(a^2) - ((y-k)^2)/(b^2) = 1

((x-h)^2)/(b^2) - ((y-k)^2)/(a^2) = 1

If the line 2x - 3y = 12 is parallel to the line ax + by = 7, what is the value of 'a'?

-3

-2

Which conic section is represented by the equation 2x^2 + 3y^2 - 4x + 6y + 7 = 0?

Ellipse

Hyperbola

Parabola

Circle

If a line has slope 2 and passes through the point (3, 4), what is the equation of the line in slope-intercept form?

y = 2x + 4

y = 2x - 4

y = 2x + 2

y = 2x - 2

If the distance between the foci of an ellipse is 10 units and its major axis is 16 units long, what is its minor axis length?

What are the coordinates of the focus of the parabola given by the equation y^2 = 4x?

(1, 0)

(0, 1)

(0, 2)

(2, 0)

#10

What is the eccentricity of the hyperbola given by the equation x^2/9 - y^2/16 = 1?

4/3

3/4

5/4

4/5

#11

What is the distance between the points (1, 2) and (-3, 5)?

√17

√21

√26

√29

#12

What is the slope of a line parallel to the line passing through the points (4, -3) and (-2, 5)?

-2

1/2

-1/2

#13

The line passing through the points (3, -1) and (5, 4) is tangent to which conic section?

Ellipse

Parabola

Hyperbola

Circle

#14

What is the equation of the line tangent to the circle x^2 + y^2 = 25 at the point (3, 4)?

y = 3x - 5

y = -3x + 5

y = 4x - 7

y = -4x + 7

#15

What is the distance between the points (-1, 2) and (3, -4)?

2√5

2√10

2√13

2√17