Find the equation of the ellipse with center (2,0), focus (5,0), b=4..

Question

tkhunny · Answer

You are given b and c.  What is the relationship to find a?

anonymous · Answer

you know it is going to look like 
$$\frac{(x-2)^2}{a^2}+\frac{y^2}{b^2}=1$$ right ?

anonymous · Answer

yes

anonymous · Answer

and you are told $b=4$ so it must be 
$$\frac{(x-2)^2}{a^2}+\frac{y^2}{16}=1$$

anonymous · Answer

yes yes..

anonymous · Answer

where's focus? hehe

anonymous · Answer

the focus evidently is $(5,0)$ because you are told
that is one of them
since it is 3 units to the right of $(2,0)$ the other is 3 units to the left, i.e. at $(-1,0)$

anonymous · Answer

this tells you  that $c=3$ and so $a^2=b^2+c^2$ gives $a^2=16+9=25$

anonymous · Answer

final answer is therefore 
$$\frac{(x-2)^2}{25}+\frac{y^2}{16}=1$$

anonymous · Answer

shall we check it?

anonymous · Answer

looks good http://www.wolframalpha.com/input/?i=ellipse+%28x-2%29^2%2F25%2By^2%2F16%3D1

anonymous · Answer

i guess the answer is 16x^2 + 25y^2 - 64x -336??

anonymous · Answer

i like my answer

tkhunny · Answer

@satellite73 's answer is particularly compelling since the last post of @silverxx is incorrect.  I didn't check the arithmetic, but it isn't an equation.  That's just not right.

anonymous · Answer

thanks!

anonymous · Answer

aaaah okay thank you so much @tkhunny @satellite73 :))