# How do you find the center, vertices, foci and eccentricity of #3x^2+4y^2-6x+16y+7=0#?

##### 1 Answer

Sep 23, 2016

See explanation.

#### Explanation:

Note the absence of xy-term. The product of the coefficients of #x^2

and y^2 = 1`2 > 0#. So, the equation represents an ellipse.

Reorganized, it becomes

Now, the center is C( 1, -2 ).

Semi axes a = 2 and b =

Eccentricity

The major axis A'CA is along

major axis.

The vertices that are at distance a = 2, from the center

So, they are at

Likewise, the foci S and S" are at distance a e = 1, from C

So, they are at

I think that these data are sufficient to make a sketch of the

ellipse...