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Marizza181 [45]
3 years ago
13

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

Mathematics
2 answers:
swat323 years ago
7 0
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
Ainat [17]3 years ago
7 0

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.

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Step-by-step explanation:

The given expression is

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