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

Question

In Exercises 49–56, identify each equation without completing the square.4x^2 - 9y^2 - 8x - 36y - 68 = 0

Accepted Answer

Hello, everyone in this video, we're going to be looking at this equation 25 X squared plus four Y squared plus 1 50 X minus eight. Y plus 1, 29 is equal to zero. And we want to determine if that equation is a circle, a parabola and ellipse or a hyperbole. And in order to do that, let's go over some of the properties that will help us determine that. So if we have a non degenerate connick section with a form A X squared plus C, Y squared plus dx plus E, Y plus F equals zero where A and C are not both zero. This equation will be a circle if A is equal to C. And it will be a problem if ACA Times C is equal to zero and it will be on a lips if A Does not equal zero And a time C is greater than zero. And finally it would be hyperbole to if A Times C is less than zero. So we're going to use these properties to help us determine what our equation is. And that starts by determining the values of A and C in our equation. So the coefficient in front of X squared for our equation is 25. So A is equal to 25. Then if we look at the coefficient in front of y squared, that is C. And for our equation coefficient in front of Y squared is four. So now I have both A and C and I can start eliminating. So I know that's not a circle because a and C are not equal to each other and A times C. Does not equal zero. So I know it's not a parabola and then AIDS is not equal C. And A times C. Is equal to 100 which is greater than zero. So it fits all the conditions to be an ellipse. And let's just check the hyperbole just in case A Times C is less than zero, which is not true because A times C. Is Greater than zero because we just determined it was 100. So the equation only fulfills the conditions to be on a lips where A does not equal C. And a time C. Is greater than zero. So phillips is the final answer that aligns with answer choice C. So hopefully this video helped and see you next time.

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In Exercises 49–56, identify each equation without completing the square.4x^2 - 9y^2 - 8x - 36y - 68 = 0

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