Rotation of a Conic Section

How do I rotate a parabola from opening up to opening horizontally?

How do I rotate the axes of and then graph

7 x^{2} - 6 \sqrt{3} x y + 13 y^{2} - 16 = 0

$7x^2 - 6sqrt3xy + 13y^2 - 16 = 0$ ?>

How do I rotate the axes of and then graph

y^{2} - 6 x^{2} - 4 x + 2 y = 0

$y^2-6x^2-4x+2y=0$ ?

How do I rotate the axes of and then graph

11 x^{2} + 5.5 y^{2} - 22 x + 11 y = 0

$11x^2+5.5y^2-22x+11y=0$ ?

How do I rotate the axes of and then graph

4 x + y^{2} + 7 y = - 4

$4x+y^2+7y=-4$ ?

How do you find the x and y axes of a function without the graph?

How do you use rotation of axes to identify and sketch the curve of

x^{2} + x y + y^{2} = 1

$x^2+xy+y^2=1$ ?

How do you use rotation of axes to identify and sketch the curve of

\sqrt{3} x y + y^{2} = 1

$sqrt3xy+y^2=1$ ?

How do you use rotation of axes to identify and sketch the curve of

97 x^{2} + 192 x y + 153 y^{2} = 225

$97x^2+192xy+153y^2=225$ ?

How do you use rotation of axes to identify and sketch the curve of

16 x^{2} - 8 \sqrt{2} x y + 2 y^{2} + (8 \sqrt{2} - 3) x - (6 \sqrt{2} + 4) y = 7

$16x^2-8sqrt2xy+2y^2+(8sqrt2-3)x-(6sqrt2+4)y=7$ ?

How do you graph the conic

x^{2} - 4 x y + y^{2} + 1 = 0

$x^2-4xy+y^2+1=0$ by first rotations the axis and eliminating the

x y

$xy$ term?

How do you graph the conic

2 x^{2} - 3 x y - 2 y^{2} + 10 = 0

$2x^2-3xy-2y^2+10=0$ by first rotations the axis and eliminating the

x y

$xy$ term?

How do you graph the conic

13 x^{2} + 6 \sqrt{3} x y + 7 y^{2} - 16 = 0

$13x^2+6sqrt3xy+7y^2-16=0$ by first rotations the axis and eliminating the xy term?

How do you graph the conic

16 x^{2} - 24 x y + 9 y^{2} - 60 x - 80 y + 100 = 0

$16x^2-24xy+9y^2-60x-80y+100=0$ by first rotations the axis and eliminating the xy term?

How do you rotate the axes to transform the equation

x y + 4 = 0

$xy+4=0$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

x^{2} + x y + y^{2} = 2

$x^2+xy+y^2=2$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

x^{2} - 4 x y + y^{2} = 1

$x^2-4xy+y^2=1$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

x^{2} + 2 \sqrt{3} x y - y^{2} = 7

$x^2+2sqrt3xy-y^2=7$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

5 x^{2} - \sqrt{3} x y + 4 y^{2} = 6

$5x^2-sqrt3xy+4y^2=6$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

x^{2} + x y = 3

$x^2+xy=3$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

2 x^{2} - x y - y^{2} = 1

$2x^2-xy-y^2=1$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

4 x^{2} - \sqrt{3} x y + y^{2} = 5

$4x^2-sqrt3xy+y^2=5$ into a new equation with no xy term and then find the angle of rotation?

How do you rotate the axes to transform the equation

2 x^{2} + \sqrt{3} x y - y^{2} = - 10

$2x^2+sqrt3xy-y^2=-10$ into a new equation with no xy term and then find the angle of rotation?

What rotation is required to remove the

x y

$xy$ -term from the conic

x^{2} + 2 \sqrt{3} x y + 3 y^{2} + 2 \sqrt{3} x - 2 y = 0

$x^2+2sqrt(3)xy+3y^2+2sqrt(3)x-2y=0$ ?

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Translation and Rotation of Axis