# The type of conic sections for the nondegenerate equations given below.a) 6x^{2} + 3x + 10y=10y^{2} + 8b) 3x^{2} + 18xy=5x + 2y + 9c) 4x^{2} + 8x - 5= -y^{2} + 6y + 3

The type of conic sections for the nondegenerate equations given below.

a)

b)

c)

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Bella

a) Consider the equation

This equation can be written as: .

It is known that the equation is in the form of

Here, the coefficient of ${x}^{2}$ and ${y}^{2}$ are $A=6$ and , which means that is, .

Therefore, the equation is of a hyperbola. Hence, the conic section of the given equation is a hyperbola.

b) Consider the equation .

This equation caan be written as: , which is in the form of .

Solve for

$=324$

This shows that Therefore, the equation is of a hyperbola. Hence, the conic section of the given equation is a heperbola.

c) Consider the equation . T

his equation can written as: . It is known that the equation is in the form Here, which means

Therefore, the equation is of an ellipse. Hence, the conic section of the given equation is an ellipse.