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Example: A circle with center at (3,4) and a radius of 6: Start with: (x−a) 2 + (y−b) 2 = r 2. Put in (a,b) and r: (x−3) 2 + (y−4) 2 = 6 2. We can then use our algebra skills to simplify and rearrange that equation, depending on what we need it for.
3 mar 2019 · Let $C$ be a circle embedded in the complex plane whose radius is $2$ and whose center is $\paren {-3, 4}$. Then $C$ can be described by the equation: $\cmod {z + 3 - 4 i} = 2$ or in conventional Cartesian coordinates: $\paren {x + 3}^2 + \paren {y - 4}^2 = 4$ Radius $4$, Center $\tuple {0, -3}$ The inequality: $\cmod {z + 3 i} > 4$
Check 'Show coordinates' and uncheck 'freeze radius'. Drag the point P to create a circle of your choice. Calculate the radius of the circle, and write the equation of the circle. Click 'show details' to check your result.
Here you will learn about the equation of a circle, including how to recognize the equation of a circle, form an equation of a circle given its radius and center, use the equation of a circle to find its center and radius, and solve problems involving the equation of a circle.
In my introductory complex analysis class, we've gone over a fair number of examples using the reciprocal function to map a line to a circle. However, we've worked only one example that used a circle as its domain, and my professor left a good portion of the problem undone.
Click in the Button Draw a Circle, then Click on map to place the center of the circle and drag at same time to start creating the circle. You can also create a circle with a fixed size. × Language
The standard equation for a circle centred at (h,k) with radius r. is (x-h)^2 + (y-k)^2 = r^2. So your equation starts as ( x + 1 )^2 + ( y + 7 )^2 = r^2. Next, substitute the values of the given point (2 for x and 11 for y), getting. 3^2 + 18^2 = r^2, so r^2 = 333. The final equation is (x+1)^2 + (y+7)^2 = 333.
