$\"\"$

The equations are $\"\"$ , $\"\"$ and $\"\"$ .

The standard form of rotated conics is $\"\"$ , where $\"\"$ .

Consider $\"\"$ .

Comapre the equation with $\"\"$ .

$\"\"$ , and $\"\"$ .

The formula $\"\"$ , can be used to determine the type of conic.

$\"\"$ .

Since $\"\"$ , the equation $\"\"$ represents a parabola. $\"\"$

Consider $\"\"$ .

Comapre the equation with $\"\"$ .

$\"\"$ , and $\"\"$ .

$\"\"$ .

Since $\"\"$ , the equation $\"\"$ represents a ellipse.

$\"\"$

Consider $\"\"$ .

Comapre the equation with $\"\"$ .

$\"\"$ , and $\"\"$ .

$\"\"$ .

Since $\"\"$ , the equation $\"\"$ represents a hyperbola. $\"\"$

A parabola has $\"\"$ line of symmetry.

Since a parabola has $\"\"$ line of symmetry, minimum angle of rotation is $\"\"$ .

An ellipse and a hyperbola have $\"\"$ lines of symmetry.

Since an ellipse and a hyperbola have $\"\"$ lines of symmetry, the minimum angle of rotation is a $\"\"$ .

$\"\"$

The completed table :

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$

A parabola has $\"\"$ line of symmetry and the minimum angle of rotation is a complete circle.

An ellipse and a hyperbola have $\"\"$ lines of symmetry and the minimum angle of rotation is a half circle.

$\"\"$

The ratation andle is $\"\"$ .

Associated with every angle drawn in standard position (except quadrantal angles) there is another angle called the reference angle.

The reference angle is the acute angle formed by the terminal side of the given angle and the $\"\"$ - axis.

Reference angles may appear in all four quadrants.

Angles in quadrant I are their own reference angles.

So, the second angle is $\"\"$ .

$\"\"$

The completed table :

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

A parabola has 1 line of symmetry and the minimum angle of rotation is a complete circle.

An ellipse and a hyperbola have 2 lines of symmetry and the minimum angle of rotation is a half circle.

The second angle is $\"\"$ .