How do you write the equation of a circle given its radius if the 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.
What is an equation of a circle with center − 2 − 1 and radius 3?
Summary: 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 equation of a circle with center 2 3 and radius 3?
The equation of the circle with center (-2,3) and radius = 3 units will be x2 + y2 + 4x - 6y + 4 = 0.
What is the equation of the circle with center (- 4 and radius 3?
Given: Center(h, k) = (-4, 3) and radius(r) = 5. ⇒ (x + 4)2 + (y - 3)2 = 25. Therefore, the equation of a circle that has its center (-4, 3) and has a radius of 5 is (x + 4)2 + (y - 3)2 = 25.
How to find the radius of a circle?
Step 1: Identify the given center of the circle. Let h be equal to the x -coordinate of this point, and let k be equal to the y -coordinate of this point. Step 2: Identify the radius of the circle, and let r equal this value . Step 3: Plug the values of h, k, and r into the general equation of a circle, and simplify.
What is the center of a circle?
Center of a Circle: The center of a circle is the point, ( x, y ), that is in the exact middle of the circle. More technically, it is the point inside the circle's edge, such that every point on the circle's edge is the same distance from that point. Radius of a Circle: The radius of a circle is a line segment that connects the center ...
How to find the radius of a circle?
Equation of a Circle in General Form 1 If g2 + f2 > c, then the radius of the circle is real. 2 If g2 + f2 = c, then the radius of the circle is zero which tells us that the circle is a point which coincides with the centre. Such type of circle is called a point circle 3 g2 + f2 <c, then the radius of the circle become imaginary. Therefore, it is a circle having a real centre and imaginary radius.
What is the distance between the centre and any point on the circumference called?
The fixed point is called the centre of the circle. The distance between the centre and any point on the circumference is called the radius of the circle.
Is a circle a function?
It is clear that a circle is not a function. Because, a function is defined by each value in the domain is exactly associated with one point in the codomain, but a line that passes through the circle, intersects the line at two points on the surface. The mathematical way to describe the circle is an equation.
Find The Center Of A Circle From An Equation
To find the center of a circle from an equation, we always want to convert to standard form.
Find The Center Of A Circle With Two Points (At Endpoints Of A Diameter)
Given two points on a circle, we may be able to find the center. If they do not lie on the same diameter, then we don’t have enough information, and we can only specify an entire family of circles, rather than one specific circle.
Find The Center Of A Circle From Three Points
To find the center of a circle from three points, we can simply substitute the x and y values from each point into the circle equation.
Find The Radius Of A Circle From An Equation
To find the radius of a circle from an equation, we always want to convert to standard form.
Find The Radius Of A Circle Given Center & Point
If we know the center of a circle and one point on the circle, we can find the radius with the distance formula.
Find The Radius Of A Circle With Two Points On The Circle
In this case, we cannot solve for a single circle, since we do not have enough information. Instead, we would get an entire family of circles that contain both points.
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What Is The Equation of A Circle?
Equation of A Circle When The Centre Is Origin
- Consider an arbitrary point P(x, y) on the circle. Let ‘a’ be the radius of the circle which is equal to OP. We know that the distance between the point (x, y) and origin (0,0)can be found using the distance formulawhich is equal to- √[x2+ y2]= a Therefore, the equation of a circle, with the center as the origin is, x2+y2= a2 Where “a” is the radius of the circle.
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, (x-h)2 + (y-k)2 = CP2 Let radius be ‘a’. Therefore, the equation of the circle with center (h, k)and the radius ‘a’is, (x-h)2+(y-k)2 = a2 which is called the standard form for the equation of a circle.
General Form of Equation of A Circle
- The general equation of any type of circle is represented by: x2+y2+2gx+2fy+c = 0, for all values of g, f and c. Adding g2+f2on both sides of the equation gives, x2+2gx+g2+y2+2fy+f2= g2+f2−c………………(1) Since, (x+g)2 = x2+ 2gx + g2 and (y+f)2 =y2 + 2fy + f2substituting the values in equation (1), we …
Polar Equation of A Circle
- To find the polar form of equation of a circle, replace the value of x = r cos θ and y = r sin θ, in x2 + y2 = a2. Hence, we get; (r cos θ)2 + (r sin θ)2 = a2 r2 cos2 θ + r2 sin2 θ = a2 r2 (cos2 θ + sin2 θ) = a2 r2 (1) = a2[Using trigonometry identity] r = a is the polar equation of a circle with radius a and center at the origin (0,0).
How to Find The Equation of The Circle?
- To find the equation of a circle given the radius and center of the circle, we can directly put the values in the standard form of the equation. (x-h)2+ (y-k)2= r2 Here, some solved problems are given to find the equation of a circle in both cases such as when the center of a circle is origin and center is not an origin is given below.
Practice Questions on Equation of Circle
- Find the equation of a circle of radius 5 units, whose centre lies on the x-axis and which passes through the point (2, 3).
- Find the equation of a circle with the centre (h, k) and touching the x-axis.
- Show that the equation x2 + y2– 6x + 4y – 36 = 0 represents a circle. Also, find the centre and radius of the circle.