Write the equation of the ellipse with center at (21), one vertex at (2-4), and one focus at (2,-2)

Step-by-step explanation:

The equation of an ellipse outside the origin is as follows

The above is for an ellipse centered on (h, k). in this case the center is in (2,1) so and

So far we have:

Now we find a and b, Where b is the semi-major axis and the minor semi-axis.

If the center is at (2, 1) and one focus is at (2,-2) this means there are 3 units of distance between the center and the focus. This quantity will be called c.

Now, of one vertex is at (2,-4) this means there are 5 units of distance between the center and the vertex, this is the semi major axis of the ellipse

⇒

and to find a:

clearing for a:

Substituting in the equation of the ellipse

wich is the second of the options.

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

3/5

step-by-step explanation:

double number line is not a standard concept, so it must have been defined in your textbook. assume top line is numerator.