Question

The equation of a circle in general form is ​ x2+y2+18x−36y+369=0 ​

Answer 1

You have to complete the square of (x²+18x+?) as well as for (y²-36y+?)

You will find: (x+9)² + (y-18)² = 36


& this is the standard equation requested

Answer 2

Answer:

$(x+9)^2+(y-18)^2=6^2$

Step-by-step explanation:

We have been given equation of a circle in general form $x^2+y^2+18x-36y+369=0$. We are asked to find the equation of the circle in standard form.

We know that equation of a circle in standard form is of format: $(x-h)^2+(y-k)^2=r^2$, where (h,k) represents the center of the circle and r represents radius.

We will convert our given equation in standard form by completing the squares as shown below:

$x^2+18x+y^2-36y+369-369=0-369$    

$x^2+18x+y^2-36y=-369$

Adding $(\frac{b}{2})^2$ to both sides of our equation we will get,

$(\frac{18}{2})^2=(9)^2=81$

$(\frac{36}{2})^2=(18)^2=324$

$x^2+18x+81+y^2-36y+324=-369+81+324$

$x^2+18x+81+y^2-36y+324=36$    

$(x+9)^2+(y-18)^2=6^2$    

Therefore, the equation of the given circle in standard form would be $(x+9)^2+(y-18)^2=6^2$.