Step 1 :  

Rotation formula :

If the x and y-axes are rotated through an angle , the coordinates  of a point P relative to the xy-plane and the coordinates of the same point relative to the new x and y-axis and are related by the formulas and .  

The general form is

The angle is

If , then , so .

If , then , so .

Step 2 : The equation is .

Compare with

and .

Substitute and in

Since , the angle lies in second quadrant.

Use Pythagorean theorem :

Step 3 :

Half angle formula of sine function is .

Substitute  in above equation.

Half angle formula of cosine function is .

Substitute  in above equation.

Step 4 : 

Rotation of x-axis :

.

Substitute  and in above equation.

Rotation of y-axis :

.

Substitute and in above equation.

The rotation formulas are  and .

Step 5 :

Substitute and in .

The above equation is a parabola.

The general form of parabolic equation is .

Where is the vertex and is focus.

Compare with .

and

The vertex is .

The focus is .

Step 6 :

The graph of the function .

Solution :

The angle is

The function .

The vertex is .

The focus is .

The graph of the function