# Conic Sections: Problems with Solutions

Problem 1
Identify the conic section represented by the equation $2x^{2}+2y^{2}-4x-8y=40$
Then graph the equation.
Problem 2
Identify the conic section represented by the equation
$4x^{2}-4xy+y^{2}-6=0$
Problem 3
Identify the conic section represented by the equation
$2x^{2}-2xy+2y^{2}=1$
Problem 4
Identify the conic section represented by the equation
$x^{2}-3xy+y^{2}=5$
Problem 5
Identify the conic section represented by the equation
$8x^{2}-8xy+2y^{2}+10\sqrt{5}x=5$
Then graph the equation.
Problem 6
Identify the conic section represented by the equation
$12x^{2}+72x+y=-109$
Graph the equation.
Problem 7
Identify the conic section represented by the equation
$x^{2}+y^{2}+10x-6y+25=0$
Graph the equation.
Problem 8
Identify the conic section represented by the equation
$x^{2}+4y^{2}=4x-y$
Graph the equation.
Problem 9
Identify the conic section represented by the equation
$x^{2}+xy+y^{2}=4$
Graph the equation.
Problem 10
Identify the conic section represented by the equation
$5x^{2}+3xy+y^{2}=44$
Graph it.

Problem 11
Identify the conic section represented by the equation
$x^{2}-2xy+y^{2}=8x+8y$
Graph the equation.
Problem 12
Identify the conic section represented by the equation
$x^{2}+4xy=16$
Problem 13
Identify the conic section represented by the equation
$x^{2}+4xy-2y^{2}-6=0$
Graph the equation.

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