Do you have difficulty in finding the center and the radius of the general form of a circle's equation? If yes, then relax. 🐛🐝
Grouping of terms with variables x and y ,and completing the squares are not needed using these shortcuts.
Are you ready to learn? ☺📚📖☺
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 x²+y²+ax+by+c=0.👍
Here is an example. 👇
What is the center and the radius of
x²+y²-2x-12y-63=0 ? 📚⏳
Given: a= -2, b= -12, and c= -63
Shortcut in finding the coordinates of the circle's center
C(h,k)= (a/-2, b/-2) 👈FORMULA👨
Substitute -2 for a and -12 for b.
C(h,k)= (1,6) ✔👍 center
Shortcut in finding the circle's radius length
Let sqrt stands for the square root.
r = sqrt(h²+k² -c) 👈FORMULA👨
Substitute 1 for h, 6 for k, and -63 for c.
r = sqrt(1² +6² -(-63))
r = sqrt(1+ 36 +63)
r = sqrt(100)
r = 10 units ✔👍 radius length
Hence, the circle's center is at point C(1,6) and its radius length 10 units.
Now, you try! ☺
Solve the center and the radius length of each circle's equation.
1. x²+y²-4x+8y-9=0 2. x²+y²+10x-18y+11=0 3. x²+y²+2y-3=0 ⏰
You can also calculate each circle's diameter, circumference and area given its computed radius length.
Author: John Paul L. Hablado, LPT