Which is the equation of a circle referenced to the coordinate origin?
103447
In R^2 = (x-a)^2 + (y-b)^2, (a,b) are the (x,y) coordinates of the center of the circle.  If you literally want to draw the circle, set the distance between the compass points to R, put the center point on (a,b) and draw.  If you want to program a computer to draw it, you create a loop where theta (the angle) goes from 0 to 2pi (one full circle) in small steps.  Then at each step, turn on the pixel nearest to (a + R*cos(theta), b + R*sin(Theta)).
794061
D stand for diameter. (You'll also see equations with R - that's radius which is half of the diameter.)  It's a straight line that crosses through the center of the circle.\n\nHere's one of many, many web sites that might help you:\n\nhttp://www.mathgoodies.com/lessons/vol2/circumference.html
1095202
The equation of a circle is:\n(x-h)^2 + (y-k)^2 = r^2\nwhere:\nh: x-coordinate of the center\nk: y-coordinate of the center\nr: Radius of the circle\n\nThe center of the circle will be midway between the points. On the x-axis:\n\n(-4 + 8)/2 = 4/2 = 2\n\nOn the y-axis:\n\n(2+8)/2 = 10/2 = 5\n\nSo the location of the center as coordinates is (2,5)\nThe radius is simply the distance from the center to either point. So, using the pathegreom theorm and the center at (h,k) and the point at (Px,Py):\n\nsqrt((h-Px)^2 + (k-Py)^2) = r\n\nUsing (8,8) for the point and the center at (2,5):\n\nsqrt((2-8)^2 + (5-8)^2) = sqrt((-6)^2 + (-3)^2) = sqrt(36 + 9) = sqrt(45)\n\nObviously, you could plug square root of 45 into your calculator to get some decimal equivilent, but it's not necessary since the equation requires r^2 anyways. So our final equation, using the form above, is:\n\n(x-2)^2 + (y-5)^2 = (sqrt(45))^2\n\nSimplifying, the square root and ^2 cancel out leaving:\n\n(x-2)^2 + (y-5)^2 = 45
351138
You got it.\n\nThe equation of a circle in standard cartesian from is:\n\n(x-a)^2+(y-b)^2=r^2\n\nThe circle is centered at (a,b) and r is the radius. For you, (a,b) is (0,0) and your r^2 term is 49, hence your r is the square root of 49 which is 7.
632411
yes u mean like the turning point of a parabolic curve...yea the x-coordinate is equal to -b/2a\nor u can differentiate the equation of the curve and put it equal to zero and solve :\neg  y = ax^2 + bx + c\ndy/dx = 2ax +b \nput this equal to zero and u get x = -b/2a
166573
:)\nNice trick question.\nYou should mention that the whole 'equations' reads:\n2 times (pi) radians = 360 degrees (measuring angles).\ntherefore (pi) radians equales 180 degrees (half circle)\nBut the number (pi) is same old 3.14......
1093431
what is d2 here..if its line what is its equation?
914363
Find the center-radious form of the equation of the circle with center = (2,-6) and the tangent to the y-axis.\n\nIf tangent to the y - axis then the point (0, -6) is the point of contact (as tangent to circle _|_ radius at point of contact)\n\nTherefore radius = 2\n\nTherefore required circle is\n\n(x - 2)² + (y + 6)² = 2²
855373
it goes around the circle twice, therefore it is a coterminal angle to the original angle.  all trig values are the same.  the only difference is that the degrees goes up by 720.\n\nadding or subtracting multiples of 2 pi just go around the circle.  since pi=180 degrees, add or subtract 180*the number of pi's.  \n\nyummy pumpkin pie :)
183039
The formula for a circle is (x-h)^2 + (y-k)^2 = r^2, so your center is (1,4).  The radius squared is 9, so the radius is 3.  So from (1,4) go up 3, down 3, left 3 and right 3.  Then connect the dots in a circle.
19668
The way to figure this out is, \n\nS=segment length of arc \nA=angle subtended by arc\nR is radius of circle \n\nS/A=2*pi*R/(2*pi),\n\nso S=RA\n\nthen differentiate with respect to time t, \n\nand dS/dt=R*dA/dt,\nand dA/dt=w, the angular speed\n\ndS/dt=T, tangential velocity\n\nso T=R*w
757335
x=r(t-sint) and y= r(1-cost) are the parametric equations of the cycloid where r is the radius of the rolling circle and t is the angle through which the radius of the circle has turned from its starting point. The angle t must be measured in radians.\n\nFor simplicity let r =1 so that we have the unit circle.\nwith t=60 = pi/3 we get\nx = pi/3-sin(pi/3) = pi/3 -(sqrt 3)/2\ny = 1-cos (pi/3) = 1- 1/2 = 1/2\n\ndy/dx= sint/(1-cost)\n=[(sqrt 3)/2]/(1/2) = 3^0.5 (at the point where t= 60= pi/3)\n\nFrom this , you can find the slope at any point define by the parameter t.\n\nb) The tangent is horizontal when t= pi and is perpendicular at the cusp which occurs at 2pi and multiples thereof. The maximum value  is 2r (or 2 for the unit circle). The length of the base of the arch is 2pi *r or just 2pi for the unit circle.
910754
the length of any line passing through the origin is sqrt(x^2 + y^2) The equation of the line is y = ax, so the length L = x*sqrt(1+a^2), and x = L/(sqrt(1+a^2).
1180944
alright, ill tell you, but not without explaining it.  im giving you the benefit of the doubt that you are not just cheating on your homework :)\n\nthe standard equation of a circle, using only variables is\n(x-h)^2 + (y-k)^2 = r^2\nwhere the center is at (h,k) and the radius is r\n\nthat means that when you look at the equation youre given, the x coordinate of the center is whatever number is subtracted from the x\n\n(x+1) ---> (x- -1)  so  h = -1\n\nyou use the same process to determine "k", which is the y coordinate of the center\n\n(y+3) ---> (y- -3)  so  k = -3\n\nthat makes the center of the circle at (-1, -3)\n\n\nfinding the radius is also simple using the standard equation. here it is again, just for reference:\n(x-h)^2 + (y-k)^2 = r^2\n\nsee how you can use that to get this?\n9/4 = r^2\n\nso just take the square root of both sides . . .\nr = +/- 3/2\n\nbecause you took the square root, the 3/2 could technically be either positive or negative, but since youre talking about the radius of a circle and you can't have a negative distance, you only take the positive answer.\n\nso r=3/2
970313
r=radius\nd=diameter\n\n1 C=2r(pi)\n2 C=d(pi)\n\n(Same thing because 2r=d)
433823
Revolving about the x-axis yields a cone whose tip is at the origin and opens in the positive x direction.  Taking discrete x slices (dx) yields a disk whose volume is given by pi*(kx)^2 dx.  Integrating from 0 to h gives us (where "S" is used as the integration symbol):\n\nV = S pi*(kx)^2 dx\n= pi * k^2 S x^2 dx\n= (pi * k^2) * (x^3)/3\n\nEvaluating from 0 to h gives us\n= (pi * k^2) * (h^3)/3 - (pi * k^2) * (0^3)/3\n= (pi * k^2 * h^3)/3
882023
The first is a sphere of radius a centered at (0,0,a) and the second is a sphere of radius a/2 centered at (0,0,a/2). Both spheres are above the xy-plane and are tangent to each other at the origin. The smaller sphere is contained inside the larger.\n\nIn spherical coordinates, the equations reduce to\nrho=2a*cos(phi) and\nrho=a*cos(phi).\n\nHence the limits are\nrho: from a*cos(phi) to 2a*cos(phi)\nphi: from 0 to pi/2\ntheta: from 0 to 2pi.\n\nI am using the mathematician's convention where phi is the angle down from the z-axis and theta is the angle from the xz-plane. Physicists use the reverse convention, so be careful!\n\nDon't forget the rho^2 sin(phi) !