What mistakes were made in solving for the equation of the ellipse?

[louie3006]

Homework Statement

an ellipse has the vertices (+&-4, 0)and the point (1,2) lies on the ellipse. find the standard form of the equation of the ellipse .

Homework Equations

(x-h)^2/a^2 + (y-k)/ b^2 = 1

The Attempt at a Solution

(x-0)^2/(4)^2 + (y-0)/b^2 = 1
(1-0)^2/16 + (2-0)^2/b^2 = 1
16b^2 ( 1/16+4/b^2=1)
**b^2 +64/16 = 16b^2
** b^2/16 + 4 = b^2
**b=b/4 + 2
note: *** is where i think i made my mistakes.
so will anyone tell me, what i did wrong and help me with how to finish this problem, thanks .

 

[rock.freak667]

Substitute the vertex first, then you'll find what a^2 works out to be.
After that, then sub in the point (1,2)

 

[mutton]

16b^2 ( 1/16+4/b^2=1)

Here, your brackets are in the wrong place and if you expand you'll see that it doesn't match the equation above it, which means your factoring was off.


$$\frac{1}{16} + \frac{4}{b^2} = 1$$

To isolate for b, move all the constants to one side and then cross multiply.