Can you tell?
Are the distances between K, K, and P, P, the
same?
Compare the distances XK, and XP,. Are these
distances the same or are they different?
Now compare the ellipses you have drawn.
Which is the larger ellipse? Why?
Explanation
Answers
Some important points and terms :-
Key Points
A circle is defined as the set of points that are a fixed distance from a center point.
The distance formula can be extended directly to the definition of a circle by noting that the radius is the distance between the center of a circle and the edge.
The general equation for a circle, centered at (a,b)(a,b) with radius rr, is the set of all points (x,y)(x,y) such that (x−a)2+(y−b)2=r2(x−a)2+(y−b)2=r2.
Pi (ππ) is the ratio of a circle’s circumference to its diameter.
Key Terms
diameter: Two times the radius of a circle.
area: The interior surface of a circle, given by A=πr2A=πr2.
circle: A two-dimensional geometric figure, consisting of the set of all those points in a plane that are equally distant from another point.
radius: A line segment between any point on the circumference of a circle and its center.
ANSWER :-
To find a formula for this, suppose that the center is the point (a,b)(a,b). According to the distance formula, the distance cc from the point (a,b)(a,b) to any other point (x,y)(x,y) is:
c=√(x−a)2+(y−b)2c=(x−a)2+(y−b)2
If we now square this equation on both sides, we have:
c2=(x−a)2+(y−b)2c2=(x−a)2+(y−b)2
Remember that the distance between the center (a,b)(a,b) and any point (x,y)(x,y) on the circle is that fixed distance, which is called the radius. So let’s change this equation so that it uses rr instead of cc.
r2=(x−a)2+(y−b)2r2=(x−a)2+(y−b)2
This is the general formula for a circle with center (a,b)(a,b) and radius rr. Notice that all we have done is slightly rearrange the distance formula equation.
Graph of a circle: The circle with center (a,b)