Question

Write the equation of the given circle. Please

Answer 1

x² + y² - 4x + 2y - 11 = 0

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!

Answer 2

Solution given.

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

another point is (6,-1)

radius (r)=
`√((6-2)²+(-1+1)²)`=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.