In Exercises 49–56, identify each equation without completing the...

Question

In Exercises 49–56, identify each equation without completing the square.4x^2 + 4y^2 + 12x + 4y + 1 = 0

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to determine the equation nine X squared plus nine Y squared minus six X minus 12, Y minus four is equal to zero. And we want to determine if that equation is a circle parabola ellipse or hyperbole to. So for this we need to remember some properties of each of these. So for a circle say that we have this sort of equation A X squared plus C, Y squared plus dx plus E, Y plus F equals zero. A circle will follow the form that A equals C. A problem will follow the form that a time C is equal to zero and ellipse will follow the form that a cannot equal C. And a time C is greater than zero. And finally a parola will follow the form that a Time C will be less than zero. So we're going to use these properties to sort of determine what our equation is. And that starts by determining what the A. Values and the C. Values are. So, in our equation you can see that the coefficient in front of X squared is nine, so A. Is equal to nine. And then the coefficient in front of the sea or the Y squared is C. And for our equation that is nine, so c. is also equal to nine. And from here you can see that A is equal to C. And that falls under the category of circle. So that becomes our final answer and notice we didn't do anything to the equation. We simply looked at the pattern and found the A. Equal C. So it has to be a circle. But hopefully this video helped and see you next time.

In Exercises 49–56, identify each equation without completing the square.4x^2 + 4y^2 + 12x + 4y + 1 = 0

Key Concepts

Quadratic Equations

Conic Sections

Standard Form of Conic Sections

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