Find the standard form of the equation of the ellipse with the given characteristics.

Mathematics

1 answer:

kicyunya [14]3 years ago

8 0

So hmm if you notice the picture below

between 2 and 16, there are 14 units, so, the center is half-way in between, thus, is at y = 7, or -2, 7

because, the major axis is over the y-axis, then the "a" component, goes under the fraction with the "y" in the numerator

$\bf \textit{ellipse, vertical major axis}\\\\

\cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1
\qquad center\ ({{ h}},{{ k}})\qquad
 vertices\ ({{ h}}, {{ k}}\pm a)\\\\
-----------------------------\\\\

\begin{cases}
b=4\\
a=7\\
h=-2\\
k=7
\end{cases}\implies \cfrac{(x+2)^2}{4^2}+\cfrac{(y-7)^2}{7^2}\implies \cfrac{(x+2)^2}{16}+\cfrac{(y-7)^2}{49}$

You might be interested in

I am very bad at math and need help with is 15÷2681

NNADVOKAT [17]

if you use a calculator the answer is 0.00559493

4 0

3 years ago

Read 2 more answers

A Ferris wheel travels in a circular motion and measures 40 meters from the top car to the bottom car. What is the length of the

Romashka-Z-Leto [24]

Answer:

20 m

Step-by-step explanation:

the distance from the top car to the bottom car is equal to the diameter of the wheel. The diameter is 40 m, and that is twice the radius. The radius of the Ferris wheel is (40 m)/2 = 20 m.

7 0

3 years ago

Read 2 more answers

Select the items the crusaders brought back with them from the East.

gulaghasi [49]

Answer:Jewels, WOOL, SILK

Step-by-step explanation:

sorry for the caps

4 0

3 years ago

Read 2 more answers

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

egoroff_w [7]

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:

$-2x^2+4x=-1$ . Now we factor out the -2:

$-2(x^2-2x)=-1$ . Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:

$-2(x^2-2x+1)=-1-2$ . Simplifying gives us this:

$-2(x^2-2x+1)=-3$

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

$-2(x-1)^2+3=y$