The area for an ellipse is given by the formula A = r1r2, where r1 and r2 are the lengths of the two radii.
If the area of an ellipse is 32 square inches with r1 measuring twice the length of r2, then what is the length of r2?
Answers
Step-by-step explanation:
The definition of a circle is as simple as the shape. A circle is the set of all points that are at a certain distance from a center point. This definition is what gives us the concept of the radius of a circle, which is equal to that certain distance.
Since we know a circle is the set of points a fixed distance from a center point, let’s look at how we can construct a circle in a Cartesian coordinate plane with variables
x
and
y
. To find a formula for this, suppose that the center is the point
(
a
,
b
)
. According to the distance formula, the distance
c
from the point
(
a
,
b
)
to any other point
(
x
,
y
)
is:
c
=
√
(
x
−
a
)
2
+
(
y
−
b
)
2
If we now square this equation on both sides, we have:
c
2
=
(
x
−
a
)
2
+
(
y
−
b
)
2
Remember that the distance between the center
(
a
,
b
)
and any point
(
x
,
y
)
on the circle is that fixed distance, which is called the radius. So let’s change this equation so that it uses
r
instead of
c
.
r
2
=
(
x
−
a
)
2
+
(
y
−
b
)
2
This is the general formula for a circle with center
(
a
,
b
)
and radius
r
. Notice that all we have done is slightly rearrange the distance formula equation.