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The conic section is represented by the equation 9x+4y^2+18x=16 is a parabola

What are conic sections?

Conic sections are figures that are formed when a plane intersects with a circular cone.

There are several types of conic sections.

Some of them include

  • Circle
  • Ellipse
  • Parabola
  • Hyperbola

How to determine the conic section?

The equation of the conic section is given as:

9x+4y^2+18x=16

Rewrite the equation by collecting the like terms

4y^2 + 9x + 18x = 16

Evaluate the like terms by adding 9x and 18x

4y^2 + 27x = 16

Subtract 27x from both sides of the equation

4y^2 = 16 - 27x

Divide both sides of the equation by 4

y^2 = 4 - 27x/4

Only parabolas take the above form

Hence, the conic section is represented by the equation 9x+4y^2+18x=16 is a parabola

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