A ruler won't help you here

Geometry Level 3

Not drawn to scale Not drawn to scale

You are given a nonrotated ellipse. This ellipse's foci are at (-4, 0) and (4, 0). What must be the value of d d , such that the length of the red line divided by the length of the orange line equals the length of the green line divided by the length of the yellow line? The yellow and orange lines are both perpendicular to x = d x= -d and x = d x = d , respectively. Enter your answer as 100 d 100d .


The answer is 625.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Hobart Pao
Feb 6, 2016

By definition, the directrices of an ellipse have the formula x = ± a e x = \pm \dfrac{a}{e} , where e e is eccentricity. We know that e = c a e = \dfrac{c}{a} , where a a is half the total length of major axis and c c is distance to focus, so we just needed to compute a 2 c \dfrac{a^{2}}{c} , or 25 4 \dfrac{25}{4} , and when we compute what the question asked for, or 100 25 4 100*\dfrac{25}{4} , we get 625 \boxed{625} .

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...