# The Faster Manual Method of Finding the Center and the Radius of the Circle's General Equation

Do you have difficulty in finding the center and the radius of the general form of a circle's equation? If yes, then relax. ππ

Be cool!π¨π¦π§πΉ

Grouping of terms with variables x and y ,and completing the squares are not needed using these shortcuts.

Are you ready to learn? βΊππβΊ

We usually look for the faster manual way or method on how to find the center and the radius of the general form of circle's equation, don't we?

The general form of the circle's equation is xΒ²+yΒ²+ax+by+c=0.π

Here is an example. π

Sample Problem:

What is the center and the radius of

xΒ²+yΒ²-2x-12y-63=0 ? πβ³

Given: a= -2, b= -12, and c= -63

Solution:

Shortcut in finding the coordinates of the circle's center

C(h,k)= (a/-2, b/-2) πFORMULAπ¨

Substitute -2 for a and -12 for b.

C(h,k)= (-2/-2),-12/-2)

C(h,k)= (1,6) βπ center

Shortcut in finding the circle's radius length

Let sqrt stands for the square root.

r = sqrt(hΒ²+kΒ² -c) πFORMULAπ¨

Substitute 1 for h, 6 for k, and -63 for c.

r = sqrt(1Β² +6Β² -(-63))

r = sqrt(1+ 36 +63)

r = sqrt(100)

r = 10 units βπ radius length

Hence, the circle's center is at point C(1,6) and its radius length 10 units.

Now, you try! βΊ

Exercises: π

Solve the center and the radius length of each circle's equation.

1. xΒ²+yΒ²-4x+8y-9=0

2. xΒ²+yΒ²+10x-18y+11=0

3. xΒ²+yΒ²+2y-3=0

β°


You can also calculate each circle's diameter, circumference and area given its computed radius length.

Author: John Paul L. Hablado, LPT

Note by John Paul Hablado
1Β year, 7Β months ago

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