## How do you complete the equation of a circle?

We know that the general equation for a circle is ( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius.

**How do you simplify a circle equation?**

Remember that the circle formula is (x – h)2 + (y – k)2 = r2. If you end up with an equation like (x + 4)2 + (y + 5)2 = 5, you have to keep straight that h and k are subtracted in the center-radius form, so you really have (x – (–4))2 + (y – (–5))2 = 5.

### What is an ellipse in precalculus?

An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two fixed points is a constant. Each fixed point is called a focus (plural: foci). We can draw an ellipse using a piece of cardboard, two thumbtacks, a pencil, and string.

**How do you graph a circle in precalculus?**

Graphing circles centered away from the origin

- Locate the center of the circle from the equation (h, v).
- 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.

#### How do you write the equation of a circle given two points?

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 equation of a hyperbola?**

The equation of a hyperbola written in the form (y−k)2b2−(x−h)2a2=1. The center is (h,k), b defines the transverse axis, and a defines the conjugate axis. The line segment formed by the vertices of a hyperbola. A line segment through the center of a hyperbola that is perpendicular to the transverse axis.

## What is a hyperbola in precalculus?

A hyperbola is the set of all points (x,y) in a plane such that the difference of the distances between (x,y) and the foci is a positive constant. Notice that the definition of a hyperbola is very similar to that of an ellipse.

**How do you find the radius of a circle from the equation?**

Where the point (h,k) gives the center of the circle, and r is the radius. We can see from the form in which the equation is expressed in the problem that the only thing different with our form is that the terms on the left side of the equation are divided by 4.

### What is the standard form for the equation of a circle?

Remember that the standard form for the equation of a circle is given by the following formula: Where the point (h,k) gives the center of the circle, and r is the radius.

**What is the equation for the circle with R=60 and center (H)?**

The equation for the circle with r=60and center (h,k)=(20,40)is (x−20)2+(y−40)2=3600. To ﬁnd the circular disc intersection with the y-axis, we have a system of two equations to work with: (x−20)2+(y−40)2= 3,600; x = 0. To ﬁnd the intersection points we simultaneously solve both equations.

#### How do you plot a circle of radius rcentered at a point?

The same reasoning can be used to show that drawing a circle of radius rcentered at a point (h,k)is the same as plotting all of the solutions of the equation: (x−h)2+(y−k)2=r2.We usually refer to the set of all solutions of the equation as the graph of the equation. x-axis y-axis (h,k) (x,y) r Figure 3.6: Deﬁning a circle.

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