Area of a circle = pi*radius squared
Circumference of a circle = 2*pi*radius or diameter*pi
The radius of the circle decreases when you make the circle smaller.
The standard equation of a circle, with center in (a,b) and radius r, is: (x-a)2 + (y-b)2 = r2
There is no such thing as a standard equation. Furthermore, there are standard forms - all different - for the equation of a line, a circle, a plane, a parabola, an ellipse and so on. the question needs to be more specific.
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Standard equation for a circle centred at the origin is x2 + y2 = r2 where r is the radius of the circle. If you increase the size of the circle then the radius must increase, so r2 will be larger. eg a circle of radius 2 has the equation x2 + y2 = 4, if the radius increases to 3 then the equation becomes x2 + y2 = 9
To find the standard equation for a circle centered at the origin, we use the distance formula to define the radius. The equation is derived from the relationship that the distance from any point ((x, y)) on the circle to the center ((0, 0)) is equal to the radius (r). Thus, the standard equation of the circle is given by (x^2 + y^2 = r^2). Here, (r) is the radius of the circle.
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The Radius
In the standard equation for a circle centered at the origin, ( x^2 + y^2 = r^2 ), the radius ( r ) determines the size of the circle. When you make the circle smaller, the radius ( r ) decreases, which in turn causes ( r^2 ) to decrease as well. Thus, the value of ( r^2 ) in the equation decreases when the circle is made smaller.
Area of a circle = pi*radius squared Circumference of a circle = 2*pi*radius or diameter*pi
The standard equation for a circle centered at the origin (0, 0) with radius ( r ) is given by ( x^2 + y^2 = r^2 ). In this equation, ( x ) and ( y ) represent the coordinates of any point on the circle, and ( r ) is the radius. This equation describes all points that are a distance ( r ) from the center.
The formula for the center of a circle is given by the coordinates ((h, k)) in the standard equation of a circle, which is ((x - h)^2 + (y - k)^2 = r^2). Here, ((h, k)) represents the center of the circle, and (r) is the radius. If the equation is presented in a different form, you can derive the center by rearranging the equation to match the standard form.