Identify each equation without completing the square.

Question

$y^2-4x-4y=0$

Accepted Answer

Hello, today we are going to be determining what conic the current equation represents without completing the square. Before we jump into the problem, we can approach this problem by using the general conic to determine what type of equation this represents. The general conic is given to us as A X squared plus cy squared plus DX plus ey minus, I'm sorry plus F is equal to zero. Now, there are four conditions that follow this generic con conic. So if the term A is equal to C or the coefficients of the X squared and Y squared terms are equal to each other, then the equation represents a circle. If the product A and C are equal to zero, then the conic represents a parabola. If the terms A is not equal to C and the product A multiplied by C is positive or in other words, greater than zero, then the conic is going to represent an ellipse. And finally, if the product A and C are less than zero or negative, the conic is going to represent a hyperbola. So now that we know the conditions of determining what conic the equation represents, let's go ahead and take a look at the given equation. The equation given to us is Y squared minus 24 X plus two Y is equal to zero. The terms that matter are going to be the X square term and the Y square term because we need those coefficients. If we take a look at our given equation, we have the Y square term which has a coefficient of one. But notice that we are missing an X squared term, we can include that X squared term by giving it a coefficient of zero. So what this means is that Arconic is going to have a coefficient of a equal to zero and a coefficient of C equal to one. Notice that if we take the product A and C together this product is going to be zero multiply by one which is zero. That means that the second condition for a parabola is satisfied, meaning that the equation given to us represents a parabola. And that means that the solution to this problem is going to be C So I hope this video helps you in understanding how to determine what comic you have without completing the square. And I'll go ahead and see you all in the next video.

Identify each equation without completing the square.
$y^2-4x-4y=0$

Key Concepts

Quadratic Equations

Standard Form of a Quadratic

Graphing Quadratics

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