Ask a New Question
Menu

uestion 1

A)A circle is drawn on a coordinate plane with the center point at (−1,3)
and a radius of 5. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

(x+1)2+(y−3)2=25
left parenthesis x plus 1 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25

(x−3)2+(y−1)2=25
left parenthesis x minus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25

(x−1)2+(y−3)2=25
left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25

(x+3)2+(y−1)2=25
left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 1 right parenthesis squared equals 25
Question 2
A)A circle is drawn on a coordinate plane with the center point at (−8,−2)
and a radius of 2. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

(x+2)2+(y+8)2=2
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y plus 8 right parenthesis squared equals 2

(x−8)2+(y−2)2=4
left parenthesis x minus 8 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 4

(x+8)2+(y+2)2=4
left parenthesis x plus 8 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 4

(x−2)2+(y−8)2=2
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 8 right parenthesis squared equals 2
Question 3
A)
Use the image to answer the question.

A circle is plotted on a coordinate plane.

Which equation is the standard form of the equation of a circle drawn on the coordinate plane, derived from the Pythagorean Theorem?

(1 point)
Responses

(x+2)2+(y−6)2=4
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared equals 4

(x−2)2+(y−2)2=4
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 4

(x−2)2+(y+2)2=16
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 16

(x−6)2+(y−2)2=16
left parenthesis x minus 6 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 16
Question 4
A)
Use the image to answer the question.

A circle is plotted on a coordinate plane.

Which equation is the standard form of the equation of a circle drawn on the coordinate plane, derived from the Pythagorean Theorem?

(1 point)
Responses

(x−4)2+(y−3)2=25
left parenthesis x minus 4 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25

(x+4)2+(y+3)2=25
left parenthesis x plus 4 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared equals 25

x2+y2=25
x squared plus y squared equals 25

x2+(y−5)2=25
x squared plus left parenthesis y minus 5 right parenthesis squared equals 25
Question 5
A)A circle is drawn on a coordinate plane with the center point at (−2,0)
and a radius of 7. Derive the equation of the circle in standard form, using the given information and the Pythagorean Theorem.(1 point)
Responses

(x−2)2+y2=49
left parenthesis x minus 2 right parenthesis squared plus y squared equals 49

x2+(y−2)2=49
x squared plus left parenthesis y minus 2 right parenthesis squared equals 49

x2+(y+2)2=49

1 answer

Let's derive the equations requested in your questions step by step using the standard form of a circle's equation, which is given by:

\[ (x - h)^2 + (y - k)^2 = r^2 \]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Question 1

Center: \((-1, 3)\)
Radius: \(5\)
Using the formula:

\[ (x + 1)^2 + (y - 3)^2 = 5^2 \]

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

Correct response: \[ (x + 1)^2 + (y - 3)^2 = 25 \]

Question 2

Center: \((-8, -2)\)
Radius: \(2\)
Using the formula:

\[ (x + 8)^2 + (y + 2)^2 = 2^2 \]

\[ (x + 8)^2 + (y + 2)^2 = 4 \]

Correct response: \[ (x + 8)^2 + (y + 2)^2 = 4 \]

Question 3

Given the choices, we have to find the correct equation. Without the image, I'll analyze the equations provided.

  1. \((x + 2)^2 + (y - 6)^2 = 4\)
  2. \((x - 2)^2 + (y - 2)^2 = 4\)
  3. \((x - 2)^2 + (y + 2)^2 = 16\)
  4. \((x - 6)^2 + (y - 2)^2 = 16\)

Without the exact coordinates, I can't directly choose the appropriate response without an image. Please check the circle's center in the image to select accordingly.

Question 4

Again, I can't directly answer without the image. If you have the coordinates for the center from the image, you can use the method described above and compare it with the options.

Question 5

Center: \((-2, 0)\)
Radius: \(7\)
Using the formula:

\[ (x + 2)^2 + (y - 0)^2 = 7^2 \]

\[ (x + 2)^2 + y^2 = 49 \]

Correct response: \[ (x + 2)^2 + y^2 = 49 \]

If you have the images or specific details regarding questions 3 and 4, it will be easier to provide accurate responses. Let me know if you have more questions!