Passing through Intersecting point of two circles and another point

Passing through Intersecting point of circle and a straight line and another point

Chord Bisected at a Point

Having a center and a tangent

dialogs

Equation of a circle passing through the origin

Input the required data of the circle.

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.

A circle passing through the origin must satisfy the condition $$c=0$$

A circle passing through the origin touching the X-axis must have it's center on the Y-axis, in the format of: $$(0,r)$$ where r is the radius of the circle. Input the radius of the circle:

A circle passing through the origin touching the Y-axis must have it's center on the X-axis, in the format of: $$(r,0)$$ where r is the radius of the circle. Input the radius of the circle:

A circle passing through the origin having center \((g,f)\) must have the radius : $$r=\sqrt{g^2+f^2}$$ where r is the radius of the circle. Input the coordinate of the point:

Theory [Equation of a circle passing through the origin]

A circle passing through the origin has its parameter \(c=0\). Alongside, it may be centered on X axis, or the Y axis, or it might be arbitrary. Being centered on X-axis and touching the origin actually refers to touching the Y axis, leading to $$f^2-c=0\Rightarrow f^2=c.$$ On the contrary, being centered on Y-axis and touching the origin actually refers to touching the X-axis, leading to $$g^2-c=0\Rightarrow g^2=c.$$ Finally, a circle having center \((g,f)\) usually, have the equation: $$(x-g)^2+(y-f)^2=g^2+f^2$$