Equations of geometric shapes

Equation of a line

$$a\cdot x+b\cdot y+c = 0$$

Find It is known that:

Equation of a line (slope-intercept)

$$y = k\cdot x+l$$

k - slope

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Equation of a line (point-slope)

$$y-y_1 = k\cdot (x-x_1)$$

k - slope
x1, y1 - point of the line

Find It is known that:

Equation of a line from two points

$$\frac{y-y_1}{y_2-y_1} = \frac{x-x_1}{x_2-x_1}$$

(x1; y1) and (x2; y2) - points of the line

Find It is known that:

Equation of a circle whose center is at (x0, y0)

$$(x-x_0)^{2}+(y-y_0)^{2} = R^{2}$$

R - radius
(x0; y0) - center of a circle

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Equation of a circle whose center is at the origin

$$x^{2}+y^{2} = R^{2}$$

R - radius

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Equation of a sphere whose center is at (x0, y0, z0)

$$(x-x_0)^{2}+(y-y_0)^{2}+(z-z0)^{2} = R^{2}$$

R - radius of a sphere
(x0; y0; z0) - center of a sphere

Find It is known that:

Equation of a sphere whose center is at the origin

$$x^{2}+y^{2}+z^{2} = R^{2}$$

R - radius of a sphere

Find It is known that: