MRK Studio
| | Dark Calculator | |
| Converters | Constants | Calculator | Analytical Geometry |
| Circle | Vectors | Straight Line | Parabola | Ellipse | Hyperbola |
| Coordinate Geometry [Triangle] | Coordinate Geometry [Quadrilateral] |
Operations:
| menu OPERATIONS: ×
In case of inputting square roots, press the square root button and activate it. To insert fractions, insert it converting into decimals. For example, \(\frac{3}{4}\) is to be inputted as \(0.75\). But the output will be in decimals. Again, for working with more irrational numbers like \(2+\sqrt3\), you must input it in decimal form using full-stop \((.)\) as the decimal point. \(x^2+y^2+2gx+2fy+c=0\) The circle has center \((-g, -f)\) and radius \(\sqrt{g^2+f^2-c}\). |
Consider that the equation of the two circles are \(g(x,y)\) and \(f(x,y)\). The third circle passes through the Intersecting points of these two circles, whose equation can be derived according to A. R. Khalifa Rule, which is: $$p(x,y)=g(x,y)+k.f(x,y)=0$$ The circle \(p(x,y)\) passes through an external point \((m,n)\) upon which none of the circles \(g(x,y)\) and \(f(x,y)\) passes through. Thus, we find \(k\): $$k=-\frac{g(m,n)}{f(m,n)}$$ Putting this k back into the former equation, we find our circle.
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