What are the equations for the circle center?
If we place the circle center at (0,0) and set the radius to 1 we get: (x−a) 2 + (y−b) 2 = r 2 (x−0) 2 + (y−0) 2 = 1 2 x2 + y2 = 1
Which is the general form of the circle equation?
Question 3: Write the general form of the circle equation with centre (2, 3) and radius 1 unit. Hence, the general form of the circle equation is x 2 + y 2 – 4x – 6y + 9 = 0.
How to calculate the coordinates of a circle?
Given that is the equation of a circle, state the coordinates of the centre and the radius. Solution . The equation is of the form where (a, b) is the centre and ris the radius. Hence, a= 6, b= −2, and r = . Example 2 . A circle has an equation 22 State the coordinates of the centre and the radius of the circle.
How is the equation of a circle satisfied?
The equation of a circle is a rule satisfied by the coordinates (“,$) of any point that lies on the circumference. Points that do not lie on the circle will not satisfy the equation. The equation of a circle will vary depending on its size (radius) and its position on the Cartesian Plane.
Which is the easiest equation to make a circle?
A circle is easy to make: Draw a curve that is “radius” away There are an infinite number of those points, here are some examples: In all cases a point on the circle follows the rule x 2 + y 2 = radius 2 Because it may not be in the neat “Standard Form” above. (x-a) 2 + (y-b) 2 = r 2 (x-0) 2 + (y-0) 2 = 1 2
Can you write a circle equation in general form?
Because it may not be in the neat “Standard Form” above. It is a circle equation, but “in disguise”! So when you see something like that think “hmm that might be a circle!” In fact we can write it in “General Form” by putting constants instead of the numbers: Note: General Form always has x2 + y2 for the first two terms.
How to calculate the radius of a circle?
Comparing (2) with (x−h)2 + (y−k)2 = a2, where (h, k) is the centre and ‘ a’ is the radius of the circle. x2 + y2 + 2gx + 2fy + c = 0, represents the circle with centre (−g,−f) and radius equal to a2 = g2 + f2− c.