Find Equation of Elipse with b=3, M(-2SQRT(5),2)

[Government$]

Homework Statement

Find equation of elips if b=3 and point M(-2SQRT(5), 2) is on elipse.

Homework Equations

x^2/a^2 + y^2/b^2 = 1

The Attempt at a Solution

x^2/a^2 + y^2/b^2 = 1

20/a^2 + 4/9 = 1

20/a^2 + 4/9 = 1 / * a^2

20 + 4a^2/9 = a^2

20 + 4^2 = 9a^2

20= 5a^2

a = 2

so equation of elipse is x^2/4 + y^2/9 = 1

But answer at the end of a book is 9x^2 + 36y^2 = 324

Which one is correct?

 

[Curious3141]

This bit:

20 + 4a^2/9 = a^2

20 + 4a^2 = 9a^2

is wrong, because you should multiply the 20 by 9 too. Equation should become

180 + 4a^2 = 9a^2, which would give you the right solution.