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Black_prince [1.1K]
3 years ago
8

Which is equation of an ellipse of an ellipse with directrices at x=4 and foci at (2,0) (-2,0)

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
7 0

Answer:

\frac{x^2}{8}  + \frac{y^2}{4}=1

Step-by-step explanation:

The directrices in this case are vertical lines, so we have a horizontal ellipse. The equation for that ellipse is:

\frac{(x - h)^2}{a^2}  + \frac{(y-k)^2}{b^2}=1

The center of the ellipse is (h,k), the diretrix is x = d and the foci are given by (h+c, k) and (h-c, k)

So, comparing the foci, we have that k = 0 and:

h + c = 2

h - c = -2

Adding these two equations, we have:

2h = 0

h = 0

c = 2

We can find the value of a^2 using the property:

c / a = a / d

Using c = 2 and d = 4, we have:

a^2 = c * d

a^2 = 8

Now, to find b^2, we use the property:

a^2 = b^2 + c^2

8 = b^2 + 4

b^2 = 4

So the equation of the ellipse is:

\frac{x^2}{8}  + \frac{y^2}{4}=1

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