Ad
related to: equation for half circle graph example with solution calculator
Search results
Results From The WOW.Com Content Network
PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
The defining property of the Carlyle circle can be established thus: the equation of the circle having the line segment AB as diameter is x(x − s) + (y − 1)(y − p) = 0. The abscissas of the points where the circle intersects the x-axis are the roots of the equation (obtained by setting y = 0 in the equation of the circle)
For example, the equations = = form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
Similarly, the radii of the given circles and a solution circle can be written as r 1, r 2, r 3 and r s, respectively. The requirement that a solution circle must exactly touch each of the three given circles can be expressed as three coupled quadratic equations for x s, y s and r s:
The equation for the drawn line is y = (1 + x)t. The equation for the intersection of the line and circle is then a quadratic equation involving t. The two solutions to this equation are (−1, 0) and (cos φ, sin φ). This allows us to write the latter as rational functions of t (solutions are given below).
Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter. Usually, the radius is denoted and required to be a positive number. A circle with = is a degenerate case consisting of a single point.
This equation can be derived directly from the geometry of the circle, or by making the parametric equation of the circle for equal to zero (the shear stress in the principal planes is always zero). Example