Step-by-step examples of finding the center and radius of circlesExample Show
Find the center and radius of the circle. ???x^2+y^2+24x+10y+160=0??? In order to find the center and radius, we need to change the equation of the circle into standard form, ???(x-h)^2+(y-k)^2=r^2???, where ???h??? and ???k??? are the coordinates of the center and ???r??? is the radius. In order to get the equation into standard form, we have to complete the square with respect to both variables. Grouping ???x???’s and ???y???’s together and moving the constant to the right side, we get ???(x^2+24x)+(y^2+10y)=-160??? Completing the square requires us to take the coefficient on the first degree terms, divide them by ???2???, and then square the result before adding the result back to both sides. The coefficient on the ???x??? term is ???24???, so ???\frac{24}{2}=12??? ???12^2=144??? The coefficient on the ???y??? term is ???10???, so ???\frac{10}{2}=5??? ???5^2=25??? Therefore, we add ???144??? inside the parentheses with the ???x??? terms, ???25??? inside the parenthesis with the ???y??? terms, and we also add ???144??? and ???25??? to the right with the ???-160???. ???(x^2+24x +144)+(y^2+10y+25)=-160 + 144+25??? Factor the parentheses and simplify the right side. ???(x+12)^2+(y+5)^2=9??? Therefore, the center of the circle is at ???(h,k)=(-12,-5)??? and its radius is ???r=\sqrt{9}=3???. Example What is the center and radius of the circle? ???6x^2+6y^2+12x-13=0??? In order to find the center and radius, we need to change the equation of the circle into standard form, ???(x-h)^2+(y-k)^2=r^2???, where ???h??? and ???k??? are the coordinates of the center and ???r??? is the radius. In order to get the equation into standard form, we have to complete the square with respect to ???x???. The ???y??? term is already a perfect square. Let’s begin by collecting like terms and moving the ???-13??? to the right. ???6x^2+12x+6y^2=13??? Our next step is to remove the coefficients of the second degree terms of the ???x??? variable and ???y??? variable. First, we’ll factor out a ???6??? then divide by ???6??? on both sides. ???6(x^2+2x+y^2)=13??? ???x^2+2x+y^2=\frac{13}{6}??? Now complete the square of the ???x??? terms. The ???y??? term is already a perfect square. ???(x^2+2x)+y^2=\frac{13}{6}??? Completing the square requires us to take the coefficient on the first degree term, divide it by ???2???, then square the result before adding the result back to both sides. The coefficient on ???x??? is ???2???, so ???\frac{2}{2}=1??? ???1^2=1??? We’ll therefore add ???1??? to both sides, and get ???(x^2+2x+1)+y^2=\frac{13}{6}+1??? Factor the ???x??? terms and simplify the right hand side. ???(x+1)^2+y^2=\frac{19}{6}??? If you want, you may also write the equation as ???(x+1)^2+(y+0)^2=\frac{19}{6}??? The center of the circle ???(h,k)??? is ???(-1,0)??? and the radius is ???\sqrt{19/6}???. Rule out ???-\sqrt{19/6}??? because a radius can't be negative. Get access to the complete Algebra 2 course'Radius of Circle Calculator' is a free online tool that calculates the radius of a circle What is Radius of Circle Calculator?The distance from the center to any point on the circumference of a circle is the radius. The size of the circle changes when the length of the radius varies. 'Radius of Circle Calculator' is a free online tool that calculates the radius of a circle within a few seconds. Radius of Circle CalculatorNOTE: Enter values for diameter, area and circumference up to 3 digits. How to Use the Radius of Circle Calculator?Follow the steps mentioned below to find the radius of a circle.
How to Calculate Radius?The radius of a circle can be calculated when the diameter is known. The formula for the radius of a circle when the diameter is given is: Radius = Diameter / 2 The radius of a circle formula when the circumference is given is: Radius = Circumference / 2п The radius of a circle formula when the area is given is: Radius = √(Area of Circle / п) Let us look at an example to understand this better.  Want to find complex math solutions within seconds? Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Book a Free Trial Class Solved Examples on Radius of Circle CalculatorExample 1: If the diameter of a circle is 7 units, find the radius. Solution: Diameter = 7 units We will use the formula of the radius. Radius = Diameter / 2 = (7/2) units = 3.5 units Example 2: If the diameter of a circle is 14 units, find the radius. Solution: Diameter = 14 units We will use the formula of the radius. Radius = Diameter / 2 = (14/2) units = 7 units Example 3: If the diameter of a circle is 24 units, find the radius. Solution: Diameter = 24 units We will use the formula of the radius. Radius = Diameter / 2 = (24/2) units = 12 units Similarly you can use the formula mentioned for finding the radius if the area and circumference of the circle are given. Now, use our online radius of circle calculator and find the radius if the circumference of a circle is
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☛ Math Calculators:Where is the center of a circle calculator?The standard equation of a circle
where C = r 2 C = r^2 C=r2, or the radius squared. With this equation, we can find the center of the circle at point ( A , B ) (A, B) (A,B).
How do you find the center radius of a circle with the center and radius?In order to find the center and radius, we need to change the equation of the circle into standard form, ( x − h ) 2 + ( y − k ) 2 = r 2 (x-h)^2+(y-k)^2=r^2 (x−h)2+(y−k)2=r2, where h and k are the coordinates of the center and r is the radius.
How do you find the center and radius from standard form?The standard form of a circle is given below: (x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius. In this case, h will be –3, k will be 6, and r will be 5.
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Identify the center and radius of the circle calculator
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