Table of Contents
How do you find the center and radius of a circle?
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.
What is center-radius form?
The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being “r”. This form of the equation is helpful, since you can easily find the center and the radius.
What is center-radius?
A circle is a set of points equidistant from a center point. Here’s a set of points equidistant from the origin! A common form to write the equation of a circle in is the center-radius form. The center-radius form is: (x−h)2+(y−k)2=r2 Here, the center point is denoted by (h,k) and r is the radius of the circle.
How do you find the radius of a circle in general form?
The general form of the equation of circle is: x2 + y2 + 2gx + 2fy + c = 0. This general form of the equation of circle has a center of (-g, -f), and the radius of the circle is r = √g2+f2−c g 2 + f 2 − c .
How did you determine the center and the radius of a circle given the equation in general form?
The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius. The circle centered at the origin with radius 1; its equation is x2+y2=1.
How do you write the equation of a circle with the center and radius?
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
What is the general form of the equation of a circle with a center at a B?
The general form of the equation of a circle with center at (a, b) and radius of length m is x2 + y2 – 2ax – 2by + (a2 + b2 – m2) = 0.
What is the standard form of the equation of a circle with center 3 and radius 4?
Summarizing: The equation of the circle with center (−3,−4) and radius 3,in standard form, is: (x+3)2+(y+4)2 = 9.
What is the equation of a circle with center 3/5 and radius 4?
Explanation: A general circle with centre (a,b) and radius r has equation (x−a)2+(y−b)2=r2 .
How do you find the radius of a circle given two points?
According to the distance formula, this is √(x−0)2+(y−0)2=√x2+y2. A point (x,y) is at a distance r from the origin if and only if √x2+y2=r, or, if we square both sides: x2+y2=r2. This is the equation of the circle of radius r centered at the origin.
What is an equation of a circle with center − 2 − 1 and radius 3?
The equation of the circle whose center is (2,1) and radius is 3 is (x – 2)2 + (y – 1)2 = 9.
What is the standard equation of a circle with center at the origin and radius 9?
So in this case since the centre is the origin, it implies that a=b=0 , and the radius r=9⇒r2=92=81 . Thus the equation reduces to x2+y2=81 .
What is the equation of the circle with center at the origin and with a radius of 9?
(x – h)² + (y – k)² = r² is the standard equation for a circle whose center is at the point (h, k) and whose radius is r. x² + y² = 81 is the equation of a circle in standard form whose center is at the origin and whose radius is 9.
What is the equation of a circle with a center at the origin and a radius of 4?
Explanation: The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2 . For a circle centered at the origin, this becomes the more familiar equation x2+y2=r2 .
Does the point 2 StartRoot 6 EndRoot lie on the circle shown?
Does the point (2,root of 6) lie on the circle shown? Explain. No, the distance from (0, 0) to (2, root of 6) is not 3 units. Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?.
What is the equation of a circle with center 5?
1 Expert Answer The equation of a circle is (x-h)2 + (y-k)2 = r2 where: (h,k) = the coordinates of the circle’s center = (5.
What is the equation of a circle with center (- 2 and radius 3?
The standard form of the equation of a circle is. where (a ,b) are the coordinates of the centre and r, the radius. Substitute these values into the standard equation. ⇒(x+2)2+(y+3)2=9 is the circle’s equation.
What is the equation of the circle whose center is at the origin and radius is 5?
x2+y2=5.
Which of these is the equation of a circle with center at the origin and radius?
x2 + y2 = r2 , and this is the equation of a circle of radius r whose centre is the origin O(0, 0). The equation of a circle of radius r and centre the origin is x2 + y2 = r2 .
Which equation of the circle has its center at the origin?
The equation of a circle, centered at the origin, is x2+y2=r2, where r is the radius and (x, y) is any point on the circle.
How will you find the radius of the circle whose center is not at the origin?
In this lesson, you learned the equation of a circle that is centered somewhere other than the origin is (x−h)2+(y−k)2=r2, where (h,k)is the center.
Which equation describes a circle with center at the origin and radius 6?
So, if the center is (0,0) and the radius is 6, an equation of the circle is: (x-0)2 + (y-0)2 = 62.
What is the radius of a circle whose equation is x2 y2 8x − 6y 21 0?
The radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0 is 5units.
What is the standard equation of a circle with center at the origin and radius is √ 2?
The standard equation for a circle: (x – a)2 + (y – b)2 = r2, where a and b are the coordinates of the origin, and r is the radius.
What is the center of the circle x² y² 4x 6y 36 0?
Now we will compare the equation withe the standard form of a circle. Then we conclude that: The center of the circle is: ( 2, -3) and the radius is 7. We can write x^2 + y^2 – 4x + 6y – 36 = 0 in the form ( x- a)^2 + (y-b)^2 = r^2, where the center of the circle is (a,b) and the radius is r.
Which equation represents a circle with a center at 3/5 and a radius of 6 units?
The equation that represents a circle with a center at (-3, -5) and a radius of 6 units is (x + 3)2 + (y + 5)2 = 36.
What is the radius of a circle whose equation is x2 y2 − 10x 6y 18 0?
The radius of the given circle is 4.
