Question: How Do You Transform A Circle Into A Function?

What is the standard form of a circle?

The graph of a circle is completely determined by its center and radius.

Standard form for the equation of a circle is (x−h)2+(y−k)2=r2.

The center is (h,k) and the radius measures r units.

This will result in standard form, from which we can read the circle’s center and radius..

How do you translate a circle on a graph?

Center away from the originLocate the center of the circle from the equation (h, v). Place the center of the circle at (3, –1).Calculate the radius by solving for r.Plot the radius points on the coordinate plane. … Connect the dots to the graph of the circle with a round, smooth curve.

What are all the formulas for a circle?

Formulas Related to CirclesDiameter of a CircleD = 2 × rCircumference of a CircleC = 2 × π × rArea of a CircleA = π × r2

Is a line a function?

For a relation to be a function, use the Vertical Line Test: Draw a vertical line anywhere on the graph, and if it never hits the graph more than once, it is a function. If your vertical line hits twice or more, it’s not a function.

Why is a circle a circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

Can you dilate a circle?

Since a circle consists of every point a certain distance away from the center of the circle, reflecting or rotating a circle would have no effect. Dilation To dilate a circle, we start with our standard equation: x2+y2=r2 To dilate the circle we multiply our desired factor squared into the right side of the equation.

How do you translate a circle to a function?

ANSWER: The center of the given circle is at the origin. The translated center will be shifted 6 units to the right and 3 units down, placing it at (6,-3). The circle has a radius of 4. The equation will be (x – 6)2 + (y + 3)2 = 16.

How do you find the standard form of a circle given two points?

Use the Distance Formula to find the equation of the circle. Substitute (x1,y1)=(h,k),(x2,y2)=(x,y) and d=r . Square each side. The equation of a circle with center (h,k) and radius r units is (x−h)2+(y−k)2=r2 .

How do you find the standard form of a circle with two endpoints?

(x−h)2+(y−k)2=r2 ( x – h ) 2 + ( y – k ) 2 = r 2 is the equation form for a circle with r radius and (h,k) as the center point. In this case, r=√26 and the center point is (2,7) . The equation for the circle is (x−(2))2+(y−(7))2=(√26)2 ( x – ( 2 ) ) 2 + ( y – ( 7 ) ) 2 = ( 26 ) 2 .

How do you tell if a graph is a function?

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

How do you convert an equation into standard form?

To convert from slope intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction.

How do you convert an ellipse into a circle?

A circle has only one radius—the distance from the center to any point is the same. To change our circle into an ellipse, we will have to stretch or squeeze the circle so that the distances are no longer the same.

Can a circle be a function?

If you are looking at a function that describes a set of points in Cartesian space by mapping each x-coordinate to a y-coordinate, then a circle cannot be described by a function because it fails what is known in High School as the vertical line test. A function, by definition, has a unique output for every input.