Write the equation of the given circle. Please

Solution given.

centre (h,k):(2,-1)

another point is (6,-1)

radius (r)==4

we have

equation of a circle is:

(x-h)²+(y-k)²=r²

(x-2)²+(y+1)²=4²

(x-2)²+(y+1)²=16is a required equation of a circle.

x² + y² - 4x + 2y - 11 = 0

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = the x-value of the center given

k = the y-value of the center given

r = radius

We know that;

h = 2

k = -1

r = 4

Now we can substitute in the values:

(x - 2)² + (y -(-1))² = 4²

(x - 2)² + (y + 1)² = 16

(x² - 4x + 4) + (y² + 2y + 1) = 16

=> x² - 4x + y² + 2y = 16 -4 - 1

=> x² - 4x + y² + 2y = 11

=> x² + y² - 4x + 2y = 11

=> x² + y² - 4x + 2y - 11 = 0 ⇒ Final Equation

I have attached the picture below of a circle of this equation, and it turns out exactly the same as the one shown in the question which tells us that the equation is correct!

Hope this helps!

mxb67

step-by-step explanation: