GRADE11 STUDENT
PLEASE HELP TO GET THE ANSWER
1.(X-9)2+(Y-6)=4
CENTER:
RADIUS:
2.(X-1)2+(XY+4)2=49
CENTER =
RADIUS:
3.(Y+3)2+(X+5)2=121
CENTER=
RADIUS=
To find the center and radius of a circle in the given equations, we need to rewrite them in standard form, which is in the form of (x-h)² + (y-k)² = r².
1. (x-9)² + (y-6) = 4
Re arrange the equation to match the standard form by expanding and collecting like terms:
x² - 18x + 81 + y² - 12y + 36 = 4
Combine like terms:
x² + y² - 18x - 12y + 117 = 0
Now, move the constant term to the other side:
x² - 18x + y² - 12y = -117
Complete the square for x by adding (18/2)² = 81 to both sides:
x² - 18x + 81 + y² - 12y = 81 - 117
Simplify:
(x - 9)² + y² - 12y = -36
To complete the square for y, add (12/2)² = 36:
(x - 9)² + y² - 12y + 36 = 0
Rearrange:
(x - 9)² + (y - 6)² = 36
From the equation, we see that the center is (9, 6) and the radius is √36 = 6.
2. (x - 1)² + (xy + 4)² = 49
Expand the equation:
x² - 2x + 1 + (xy)² + 8xy + 16 = 49
Combine like terms:
x² - 2x + (xy)² + 8xy + 1 + 16 = 49
Rearrange:
x² - 2x + (xy)² + 8xy + 17 = 49
Simplify:
x² - 2x + (xy)² + 8xy = 49 - 17
Rearrange:
x² - 2x + (xy)² + 8xy = 32
This equation does not have the standard form of a circle, so we cannot determine its center and radius using the information given.
3. (y + 3)² + (x + 5)² = 121
Re arrange the equation:
(y + 3)² + (x + 5)² = 121
This equation is already in standard form.
From the equation, we can see that the center is (-5, -3) and the radius is √121 = 11.
To summarize:
1. Center: (9, 6)
Radius: 6
2. Equation cannot be expressed in the standard form of a circle.
3. Center: (-5, -3)
Radius: 11