Table of Contents
How will you determine the equation of the circle given the center and radius?
Example. x 2 + y 2 + 2 g x + 2 f y + c = 0 is used to work out the centre of the circle, and the radius. ( x − a ) 2 + ( y − b ) 2 = r 2 is used to write the equation of the circle when you know the centre and the radius.
How do you find the equation of a circle on a graph?
The equation of a circle appears as (x – h)2 + (y – v)2 = r2. This is called the center-radius form (or standard form) because it gives you both pieces of information at the same time. The h and v represent the coordinates of the center of the circle being at the point (h, v), and r represents the radius.
How do you find the equation of a circle with center?
The equation of circle with (h,k) center and r radius is given by: (x-h) 2 + (y-k) 2 = r 2. Thus, if we know the coordinates of the center of the circle and its radius as well, we can easily find its equation. Example: Say point (1,2) is the center of the circle and radius is equal to 4
What is the centre of a circle in the 3rd quadrant?
Let the circle beg, f, c so that its centre (- g, – f) is in 3rd quadrant so that both g and fare to be + ive. Centre lies on x – y – 1 = 0
How do you find the radius of a circle on x axis?
The circle touches x axis, so that radius of the circle=k. Coordinates of centre are (2 , 1 ) in 1st quadrant and (-2 , 5) in 2nd quadrant (which is not required). Let (h,k) be the coordinate of the centre of circle which lie on the line x+y=3. Therefore h+k=3…………………. (1) The circle touches x axis, so that radius of the circle=k.
What is the radius of a circle if the centre is not?
Equation of a Circle When the Centre is not an Origin Let C(h, k) be the centre of the circle and P(x, y) be any point on the circle. Therefore, the radius of a circle is CP. By using distance formula,