Question

What are the directrices of the ellipse given by the equation x^2/36+y^2/100=1

Answer 1

\[\frac{ x^2 }{ 36 }+\frac{ y^2 }{ 100 }=1\]

Answer 2

Choices:

x= +-5/8
y= +-5/8
x= +-25/2
y= +-25/2

Answer 3

directrix of an ellipse will be at \(\large \cfrac{a^2}{c}\) distance from the center of the ellipse

Answer 4

so, which one above would be your "a" ?

Answer 5

bearing in mind that the "c" distance from the center to a focus is
\(\large c^2 = a^2-b^2\)

Answer 6

36?

Answer 7

for an ellipse the "a" element is the "bigger one" of the 2 denominators, and at the "axis" is where the ellipse has its major axis

Answer 8

So a would be 100

Answer 9

right, so what would you get for "c" off \(\large c=\sqrt{a^2-b^2}\)

Answer 10

1? Not sure.

Answer 11

well, your elipse equation is
$$
\cfrac{ x^2 }{ \color{red}{36} }+\cfrac{ y^2 }{ \color{red}{100} }=1 \implies \cfrac{ (x-h)^2 }{ \color{red}{b^2} }+\cfrac{ (y-k)^2 }{ \color{red}{a^2} }=1
$$

Answer 12

keep in mind that 36 and 100 are in squared form if you were to write them without the squared version, they'd be
$$
\cfrac{ x^2 }{ \color{red}{6^2} }+\cfrac{ y^2 }{ \color{red}{10^2} }=1 \implies \cfrac{ (x-h)^2 }{ \color{red}{b^2} }+\cfrac{ (y-k)^2 }{ \color{red}{a^2} }=1
$$