Question 1

A circle is defined by the equation

(x - 3)^2 + (y + 1)^2 = 25

. At which point does the line with a slope of

m = 0

passing through the center of this circle intersect the y-axis?

Accepted Answer

Answer

Answer

Answer

Question 2

A system of equations consists of the line

(x - 3)^2 + (y + 1)^2 = 25

and a circle centered at the origin with a radius of

m = 0

. At how many points does the line intersect the circle?

Accepted Answer

1

Answer

Infinitely many

Answer

2

Answer

0

Question 3

The center of a circle is located at the intersection of the lines

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. If the circle is tangent to the x-axis, what is its equation?

Accepted Answer

Answer

Answer

Answer

Question 4

Two circles are given by the equations

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. A line passes through the origin

(0,0)

and the center of the second circle. What is the slope of this line and does it intersect the first circle?

Accepted Answer

The slope is 0 and it intersects the first circle at two points.

Answer

The slope is 0 and it is tangent to the first circle at one point.

Answer

The slope is 6 and it does not intersect the first circle.

Answer

The slope is undefined and it intersects the first circle at two points.

Question 5

A circle is centered at

(x - 3)^2 + (y + 1)^2 = 25

and is tangent to the line

m = 0

. If a second line is drawn through the center of the circle with a slope perpendicular to the tangent line, what is the equation of this second line in slope-intercept form?

Accepted Answer

Answer

Answer

Answer

Question 6

The equations of two lines are given by

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. Their point of intersection is the center of a circle that is tangent to the y-axis. What is the equation of this circle?

Accepted Answer

Answer

Answer

Answer

Question 7

A circle has the equation

(x - 3)^2 + (y + 1)^2 = 25

. A line with a slope of

m = 0

passes through the point

(0,0)

. At which other point does this line intersect the circle?

Accepted Answer

Answer

Answer

Answer

Question 8

A circle is defined by the equation

(x - 3)^2 + (y + 1)^2 = 25

. A line with a slope of

m = 0

passes through the center of this circle. What is the y-intercept of this line?

Accepted Answer

Answer

Answer

Answer

Question 9

A line is tangent to the circle

(x - 3)^2 + (y + 1)^2 = 25

at the point

m = 0

. What is the slope of this tangent line?

Accepted Answer

Answer

Answer

Answer

Question 10

The center of a circle is found at the intersection of the system

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. If this circle has a radius of 4, what is the correct equation of the circle?

Accepted Answer

Answer

Answer

Answer

Question 11

A system of equations consists of the line

(x - 3)^2 + (y + 1)^2 = 25

and the circle

m = 0

. At which points does the line intersect the circle?

Accepted Answer

(0, -1)

and

(-4, -3)

Answer

(0, -1)

and

(-4, -3)

Answer

(0, -1)

and

(-4, -3)

Answer

(0, -1)

and

(-4, -3)

Question 12

A line is tangent to the circle

(x - 3)^2 + (y + 1)^2 = 25

at the point

m = 0

. What is the slope of this tangent line?

Accepted Answer

Answer

Answer

Answer

Question 13

Which of the following lines is perpendicular to the line passing through the center of the circle

(x - 3)^2 + (y + 1)^2 = 25

and the origin?

Accepted Answer

Answer

Answer

Answer

Question 14

A line with a slope of

(x - 3)^2 + (y + 1)^2 = 25

passes through the center of the circle defined by

m = 0

. What is the equation of this line in slope-intercept form?

Accepted Answer

Answer

Answer

Answer

Question 15

The circle

(x - 3)^2 + (y + 1)^2 = 25

and the line

m = 0

intersect at two points. What is the length of the chord formed by these two intersection points?

Accepted Answer

Answer

Answer

Answer

Question 16

A circle is defined by the equation

(x - 3)^2 + (y + 1)^2 = 25

. A line passes through the center of this circle and is perpendicular to a second line given by

m = 0

. What is the equation of the line passing through the center?

Accepted Answer

Answer

Answer

Answer

Question 17

The diameter of a circle has endpoints at

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. What is the equation of this circle?

Accepted Answer

Answer

Answer

Answer

Question 18

The circle

(x - 3)^2 + (y + 1)^2 = 25

and the line

m = 0

intersect at the point

(0,0)

. What is the value of

m

and what is the other intersection point of the system?

Accepted Answer

(0, -1)

and the point is

(-4, -3)

Answer

(0, -1)

and the point is

(-4, -3)

Answer

(0, -1)

and the point is

(-4, -3)

Answer

(0, -1)

and the point is

(-4, -3)

Question 19

Which of the following lines is a secant line that intersects the circle

(x - 3)^2 + (y + 1)^2 = 25

at exactly two points?

Accepted Answer

Answer

Answer

Answer

Question 20

Two circles are defined by the equations

(x - 3)^2 + (y + 1)^2 = 25

and

m = 0

. What is the equation of the line that passes through the two points of intersection of these circles?

Accepted Answer

Answer

Answer

Answer

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