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

Question

In Exercises 49–56, identify each equation without completing the square.100x^2 - 7y^2 + 90y - 368 = 0

Accepted Answer

Hey everyone in this problem, we are asked to determine what the given equation represents without completing the square. Okay, so the equation we're given is 25 X squared minus 78. Y squared plus 16. Y minus 112 is equal to zero. Okay, now let's recall that we have a general equation. A X squared plus C, Y squared plus D X plus E Y plus F equals zero. Okay, now we can compare this to our equation. We have A is out front of the X squared term. So in our case A is 25. We have see out front of the y squared term. So in our case C is negative 78. We have D in front of the X. Term which we don't have. Okay, so D. Is just zero. In our case we have E. In front of the Y. Term which in our case is And then we have f. The constant by itself. Which in our case is 112. All right. So when we have this general equation, we have certain conditions on these parameters A, C, D, E and F. That tell us what type of equation this is. Okay, so first things first we need both A and C. Not to be zero. Okay, If A N C. If A equals zero and C equals zero, then we have linear case. Okay, we don't want to worry about the linear case. So otherwise what happens? Hey, well, we know A and C. Are not both zero. So what do we have? Well, what about if A is equal to C? Okay, If a is equal to C. This is going to be a circle determine front of the X squared. The coefficient in front of the Y squared are the same. This is a circle. If a times C is equal to zero. Okay, well that means that one of them is equal to zero. We're gonna get a problem. Okay, so say that C is equal to zero. Well now we just have Y. Okay, we move the Y over is equal to something X squared something X in a constant. Okay, so this is just a problem and that's not what we have either. Neither A nor cr zero. Okay, so we don't have this case. We don't have this case. What other cases do we have? What if A is not equal to C? Okay, so we don't have a circle But the product AC. Is bigger than zero. Well, in that case we have an ellipse. Okay, if a times C is bigger than zero, that means A and C have the same sign. We have an ellipse. Well, in our case A and C have different signs. So their product will be negative. So we don't have this case either. Okay, so we have the case where A C. is less than zero, A times c. times -78. That is less than zero. And so this is going to be hyperbole. Okay, Alright, so in our case we have this case a hyperbole A is 25 C is negative 78. Their product is less than zero. We get D. A. Hyperbole. Thanks everyone for watching. I hope this video helped see you in the next one.

Struggling with College Algebra?

In Exercises 49–56, identify each equation without completing the square.100x^2 - 7y^2 + 90y - 368 = 0

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