Question 1

Find the center and radius of the circle with equation (x + 14)² + y² = 45. A) center = (-14, 0), r = 45 B) center = (-14, 0), r = C) center = (14, 0), r = 45 D) center = (14, 0), r =

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Question 2

The point (6, 0) lies on a circle centered at (-2, 5). Find the equation of the circle in standard form. A) (x + 2)² + (y - 5)² = 89 B) (x + 2)² + (y - 5)² = 64 C) (x - 2)² + (y + 5)² = 89 D) (x - 2)² + (y + 5)² = 64

Accepted Answer

The equation of a circle in standard form is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Given the center (-2, 5) and a point on the circle (6, 0), we can find the radius by calculating the distance between these two points: sqrt((6 - (-2))^2 + (0 - 5)^2) = sqrt(8^2 + 5^2) = sqrt(64 + 25) = sqrt(89). Thus, the equation is (x + 2)^2 + (y - 5)^2 = 89.

Question 3

The point (6, -6) lies on a circle centered at (0, 1). Find the equation in standard form. A) x² + (y - 1)² = 85 B) x² + (y + 1)² = 85 C) (x + 1)² + y² = 85 D) (x - 1)² + y² = 85

Accepted Answer

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. The distance from the center (0, 1) to the point (6, -6) is sqrt((6-0)^2 + (-6-1)^2) = sqrt(36 + 49) = sqrt(85), so r^2 = 85. Thus, the equation is (x - 0)^2 + (y - 1)^2 = 85, which simplifies to x^2 + (y - 1)^2 = 85.

Question 4

The point (-2, -4) lies on a circle centered at (6, 1). Find the equation of the circle in standard form. A) (x + 6)² + (y + 1)² = 89 B) (x - 6)² + (y - 1)² = 89 C) (x - 6)² + (y - 1)² = 7 D) (x + 2)² + (y + 4)² = 89

Accepted Answer

The standard form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. The distance between the center (6, 1) and the point (-2, -4) is the radius, calculated using the distance formula: sqrt((6 - (-2))^2 + (1 - (-4))^2) = sqrt(8^2 + 5^2) = sqrt(64 + 25) = sqrt(89). Thus, the equation is (x - 6)^2 + (y - 1)^2 = 89.

Question 5

Find the equation of the circle with radius 5 and center (16, -13) in standard form.

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Question 6

Find the center and radius of the circle with equation (x - 16)² + (y + 18)² = 16.

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Question 7

Transform the equation
  into standard form by completing the square. State the center and radius.

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  into standard form...

Question 8

If a cellular phone tower has a reception radius of 190 miles and you live 50 miles north and 220 miles east of the tower, can you use your cell phone while at home?

Accepted Answer

The distance from the tower to your home can be calculated using the Pythagorean theorem, $d = \sqrt{(50^2 + 220^2)}$, which equals approximately 225.83 miles, which is beyond the 190-mile reception radius of the tower.

Question 9

State the center and radius of the equation 
  
 .

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Question 10

State the center and radius of the equation 
  
 .

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Question 11

Express the equation   in standard form.

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Question 12

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 50x² - 31y² = 29

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Question 13

Identify the conic section as a parabola, ellipse, circle, or hyperbola.
The set of all points equidistant from the point (13, -18) and from the line x = -13

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Question 14

Identify the conic section as a parabola, ellipse, circle, or hyperbola.
The set of all points whose distance from the point (6, -9) plus the distance from the point (12, -9) is exactly 31 units.

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Question 15

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 64x² + 9y² = 36

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Question 16

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. x² - y = -6

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Question 17

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 25x² - 100y² = 64

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Question 18

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 3x² - 2x + 10y² - 6y + 19 = -9

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Question 19

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. -12x² - 18x - y = 4

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Question 20

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 8x² - 6x - 12y² + 4y + 5 = 7

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Quiz 3: Linear, Quadratic, Polynomial, and Rational Functions

Find the center and radius of the circle with equation (x + 14) ² + y² = 45.

The point (6, 0) lies on a circle centered at (-2, 5) . Find the equation of the circle in standard form.

The point (6, -6) lies on a circle centered at (0, 1) . Find the equation in standard form.

The point (-2, -4) lies on a circle centered at (6, 1) . Find the equation of the circle in standard form.

Find the equation of the circle with radius 5 and center (16, -13) in standard form.

Find the center and radius of the circle with equation (x - 16)² + (y + 18)² = 16.

Transform the equation into standard form by completing the square. State the center and radius.

If a cellular phone tower has a reception radius of 190 miles and you live 50 miles north and 220 miles east of the tower, can you use your cell phone while at home?

State the center and radius of the equation .

State the center and radius of the equation .

Express the equation in standard form.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 50x² - 31y² = 29

Identify the conic section as a parabola, ellipse, circle, or hyperbola. The set of all points equidistant from the point (13, -18) and from the line x = -13

Identify the conic section as a parabola, ellipse, circle, or hyperbola. The set of all points whose distance from the point (6, -9) plus the distance from the point (12, -9) is exactly 31 units.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 64x² + 9y² = 36

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. x² - y = -6

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 25x² - 100y² = 64

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 3x² - 2x + 10y² - 6y + 19 = -9

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. -12x² - 18x - y = 4

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 8x² - 6x - 12y² + 4y + 5 = 7

Quiz 3: Linear, Quadratic, Polynomial, and Rational Functions

Find the center and radius of the circle with equation (x + 14) 2 + y2 = 45.

The point (6, 0) lies on a circle centered at (-2, 5) . Find the equation of the circle in standard form.

The point (6, -6) lies on a circle centered at (0, 1) . Find the equation in standard form.

The point (-2, -4) lies on a circle centered at (6, 1) . Find the equation of the circle in standard form.

Find the equation of the circle with radius 5 and center (16, -13) in standard form.

Find the center and radius of the circle with equation (x - 16)2 + (y + 18)2 = 16.

Transform the equation into standard form by completing the square. State the center and radius.

If a cellular phone tower has a reception radius of 190 miles and you live 50 miles north and 220 miles east of the tower, can you use your cell phone while at home?

State the center and radius of the equation .

State the center and radius of the equation .

Express the equation in standard form.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 50x2 - 31y2 = 29

Identify the conic section as a parabola, ellipse, circle, or hyperbola. The set of all points equidistant from the point (13, -18) and from the line x = -13

Identify the conic section as a parabola, ellipse, circle, or hyperbola. The set of all points whose distance from the point (6, -9) plus the distance from the point (12, -9) is exactly 31 units.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 64x2 + 9y2 = 36

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. x2 - y = -6

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 25x2 - 100y2 = 64

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 3x2 - 2x + 10y2 - 6y + 19 = -9

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. -12x2 - 18x - y = 4

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 8x2 - 6x - 12y2 + 4y + 5 = 7

Find the center and radius of the circle with equation (x + 14) ² + y² = 45.

Find the center and radius of the circle with equation (x - 16)² + (y + 18)² = 16.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 50x² - 31y² = 29

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 64x² + 9y² = 36

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. x² - y = -6

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 25x² - 100y² = 64

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 3x² - 2x + 10y² - 6y + 19 = -9

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. -12x² - 18x - y = 4

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 8x² - 6x - 12y² + 4y + 5 = 7