My Math Forum Ellipse question

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 April 24th, 2012, 04:15 AM #1 Newbie   Joined: Apr 2012 Posts: 1 Thanks: 0 Ellipse question Hi i am new to this forum, and the main reason that i joined here is that my maths is very weak. I wanted to know if any of you could provide me with valuable tips to improve on my maths. here is the question btw. if P is a point on the ellipse, x^2/16 + y^2/20 =1 . whose focii are S and S' then find PS + PS' i would be grateful if someone could answer both my queries. thanks
April 24th, 2012, 05:12 AM   #2
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Joined: Dec 2011

Posts: 277
Thanks: 1

Re: Ellipse question

An ellipse is defined by two points, each called a focus. (F1, F2).

If you take any point on the ellipse, the sum of the distances to the focus points is a constant.

The general formula for an ellipse with its major axis parallel to the vertical axis has the form $\frac{y^2}{a^2}+\frac{x^2}{b^2}=1$ where $a>b.$

If P is a point on the ellipse $\frac{y^2}{a^2}+\frac{x^2}{b^2}=1$ whose foci are F1 and F2 then
$PF_1 + PF_2=2a$

In our case we have
$\frac{x^2}{16} +\frac{y^2}{20}=1$

$\frac{y^2}{20}+\frac{x^2}{16}=1$

$\frac{y^2}{(\sqrt{20})^2}+\frac{x^2}{4^2}=1$

Thus,
$a=\sqrt{20}$
and
$PS + PS' =2a=2\sqrt{20}=2\sqrt{4.5}=2.2\sqrt{5}=4\sqrt{5}$

Quote:
 Originally Posted by indianmathnoob Hi i am new to this forum, and the main reason that i joined here is that my maths is very weak. I wanted to know if any of you could provide me with valuable tips to improve on my maths.

 Tags ellipse, question

### if p is a point on the ellipse whose foci are s and s'. then ps ps' is

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