Question

Identify the type of conic section whose equation is given and find the vertices and foci.

x^2 = 4y - 2y^2

Answer 1

 Step 1 :

Identify the conic from its general equation :

The graph of is one of the following

1. Circle :

2. Parabola : , (either or but not both).

3. Ellipse : , ( A and C have like signs).

4. Hyperbola : , ( A and C have unlike signs).

 Step 2 :

The equation is .

Rewrite the equation :

Compare with the general equation .

and A,C  are having like signs.

The graph of the equation represents an ellipse.

Answer 2

contd.....

Step 3 :

The ellipse equation is .

Rewrite the equation into standard form of ellipse : 

Compare it to standard form of vertical ellipse is .

Where

a  is length of semi major axis and b is length of semi minor axis.

Center is , vertices .

Foci .

Where .

Now compute the c :

vertices :

 

Foci :

Solution :

(a) The graph of the equation represents an ellipse.

(b) Vertices and Foci .