Answer each question. A line passes through the points of interse...

Question

Answer each question. A line passes through the points of intersection of the graphs of y = x^2 and x^2 + y^2 = 90. What is the equation of this line?

Accepted Answer

Hey, everyone in this problem, we're asked to find the equation of a line passing through the intersection of Y is equal to three X squared divided by 50 and X squared plus Y squared is equal to 136 given a figure here. And we're gonna come back to that in just a minute. We have four answer choices. Option A X is equal to six. Option B Y is equal to negative 10. Option C negative 10, X plus six, Y is equal to zero. And option D Y is equal to six. So we look at this figure that we're given and we have this green circle drawn on our graph and we're told that it has equation X squared plus Y squared equals 136. OK. So that's that second equation we were given in the problem. And in red, we have this parabola with equation Y is equal to three X squared divided by 50. So we want to find the equational line passing through the intersection of these two graphs. Now, if we look at these curves on our graph, we see that we have an intersection point at negative 10 comma six and an intersection point at 10 comma six. So if we want to find the equation of a line passing through that intersection, I am gonna draw in blue and we're just gonna connect those two points with a line. And what you can see is that because these two points both have the same Y value the line we draw that intersects the two of them is just a horizontal line. So we have a horizontal line here and we can see from our graph that it's at a Y value of six, we can also see that from the um intersection points. And so the equation on the line is just gonna be Y it is equal to six a horizontal line. And so our answer choice here is gonna be option D Y is equal to six that horizontal line connecting those intersection points. That's it for this one. Thanks everyone for watching. See you in the next video.

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Answer each question. A line passes through the points of intersection of the graphs of y = x^2 and x^2 + y^2 = 90. What is the equation of this line?