Free Printable Pre-calculus Quiz 1 (Circle and Ellipse)

1.

Is the set of all points in a plane equidistant from a fixed point.

a)

Circle

b)

Parabola

c)

Ellipse

d)

Hyperbola

2.

It is the set of all points in a plane the sum of whose distance from two fixed points in the plane (the foci) is constant.

a)

Raduis

b)

Circle

c)

Focus

d)

Ellipse

3.

It is the distance from 1 co-vertex to another co-vertex.

a)

Major Axis

b)

Minor Axis

c)

Semi-Major Axis

d)

Semi-Minor Axis

4.

It is the ratio of the distance from the center to the foci and the distance from the center to the vertices.

a)

Arc

b)

Major Axis

c)

Eccentricity

d)

Minor Axis

5.

These are the two reference points of the locus of points that form the ellipse that we know.

a)

Focus

b)

Vertex

c)

Co-Vertex

d)

Center

6.

Find the Radius of the following equation

$\left(x-2\right)^2+\left(y+1\right)^2=16$

a)

1

b)

2

c)

3

d)

4

7.

Find the Center of the following equation

$\left(x-2\right)^2+\left(y+1\right)^2=16$

a)

(-2,1)

b)

(2,-1)

c)

(2,1)

d)

(-2,-1)

8.

Find the radius of a circle given a point $\left(2,2\right)$ lies on the circle and center at $\left(3,5\right)$

a)

$\sqrt[]{11}$

b)

$-\sqrt[]{11}$

c)

$\sqrt[]{10}$

d)

$\sqrt[]{7}$

9.

Write the standard equation of a circle given a point $\left(2,2\right)$ lies on the circle and center at $\left(3,5\right)$

a)

$\left(x-3\right)^2+\left(y-5\right)^2=12$

b)

$\left(x-3\right)^2+\left(y-5\right)^2=9$

c)

$\left(x-3\right)^2+\left(y-5\right)^2=10$

d)

$\left(x-3\right)^2+\left(y-5\right)^2=11$

10.

Write the standard equation of a circle given the equation

$x^2+y^2+6x-10y-15=0$

a)

$\left(x+3\right)^2+\left(y+5\right)^2=49$

b)

$\left(x-3\right)^2+\left(y-5\right)^2=49$

c)

$\left(x-3\right)^2+\left(y+5\right)^2=49$

d)

$\left(x+3\right)^2+\left(y-5\right)^2=49$

11.

Find the Center of a circle given the equation

$x^2+y^2+6x-10y-15=0$

a)

(3,-5)

b)

(-3,5)

c)

(3,5)

d)

(-3,-5)

12.

Find the center of an ellipse given

$Foci:\ \left(4,1\right)\ and\ \left(-6,1\right)$

$Vertex\ \left(6,1\right)\ and\ \left(-8,1\right)$

a)

$\left(1,-1\right)$

b)

$\left(1,1\right)$

c)

$\left(-1,1\right)$

d)

$\left(-1,-1\right)$

13.

Write the Standard equation of an ellipse given

$Foci:\ \left(4,1\right)\ and\ \left(-6,1\right)$

$Vertex\ \left(6,1\right)\ and\ \left(-8,1\right)$

a)

$\frac{\left(x+1\right)^2}{49}+\frac{\left(y-1\right)^2}{72}=1$

b)

$\frac{\left(x+1\right)^2}{49}+\frac{\left(y-1\right)^2}{24}=1$

c)

$\frac{\left(x-1\right)^2}{49}+\frac{\left(y-1\right)^2}{72}=1$

d)

$\frac{\left(x-1\right)^2}{49}+\frac{\left(y-1\right)^2}{24}=1$

14.

FInd the Distance of the Semi-Minor Axis of an ellipse given

$Foci:\ \left(4,1\right)\ and\ \left(-6,1\right)$

$Vertex\ \left(6,1\right)\ and\ \left(-8,1\right)$

a)

$2\sqrt[]{6}$

b)

$6\sqrt[]{2}$

c)

$3\sqrt[]{5}$

d)

$5\sqrt[]{3}$

15.

Write the standard equation of an ellipse given:

Major Vertical Axis = 12

Minor Horizontal Axis = 8

Center (-1,2)

a)

$\frac{\left(x+1\right)^2}{144}+\frac{\left(y-2\right)^2}{64}=1$

b)

$\frac{\left(x+1\right)^2}{64}+\frac{\left(y-2\right)^2}{144}=1$

c)

$\frac{\left(x+1\right)^2}{36}+\frac{\left(y-2\right)^2}{16}=1$

d)

$\frac{\left(x+1\right)^2}{16}+\frac{\left(y-2\right)^2}{36}=1$

16.

Find the Center of an ellipse given:

$x^2+4y^2-2x+16y-19=0$

a)

(-1,2)

b)

(1,-2)

c)

(2,-4)

d)

(-2,4)

17.

Find the Foci of an ellipse given:

$x^2+4y^2-2x+16y-19=0$

a)

$\left(-1+3\sqrt[]{3},-2\right)\ and\ \left(-1-3\sqrt[]{3},-2\right)$

b)

$\left(-1+3\sqrt[]{2},\ 2\right)\ and\ \left(-1-3\sqrt[]{2},\ 2\right)$

c)

$\left(1+3\sqrt[]{3},\ 2\right)\ and\ \left(1-3\sqrt[]{3},\ 2\right)$

d)

$\left(1+3\sqrt[]{3},-2\right)\ and\ \left(1-3\sqrt[]{3},-2\right)$

18.

Find the Eccentricity of an ellipse given:

$x^2+4y^2-2x+16y-19=0$

a)

$\frac{\sqrt[]{3}}{3}$

b)

$\frac{\sqrt[]{3}}{2}$

c)

$\frac{\sqrt[]{2}}{2}$

d)

$\frac{\sqrt[]{2}}{3}$

19.

Find the Center of an ellipse given:

$2x^2+9y^2+8x-18y-19=0$

a)

(2,-1)

b)

(1,-2)

c)

(-2,1)

d)

(-1,2)

20.

Find the length of the Major Horizontal Axis of an ellipse given:

$2x^2+9y^2+8x-18y-19=0$

a)

$6\sqrt[]{2}$

b)

8

c)

$2\sqrt[]{6}$

d)

$6\sqrt[]{6}$

Pre-calculus Quiz 1 (Circle and Ellipse)

Total questions: 20

Worksheet time: 10mins

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