Solving the System: x^2+(y-5)^2=9 and y=x^2+K

Thread starter answerseeker
Start date Oct 2, 2005
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The discussion focuses on solving the system of equations x^2 + (y - 5)^2 = 9 and y = x^2 + K, where K > 0. The first equation represents a circle centered at (0, 5) with a radius of 3, while the second equation describes a parabola. Participants suggest sketching the graphs to better understand the intersections, which will help determine the conditions for having four solutions or no solutions. The conversation emphasizes the importance of visualizing the curves to analyze their intersections effectively. Understanding the relationship between the circle and parabola is crucial for finding the values of K that yield the desired number of solutions.

Oct 2, 2005

answerseeker

Q: If K>0, for what values of k does the system x^2+ (y-5)^2=9 and y=x^2 +K have:

a) 4 solutions
b) no solution

i have no idea how to begin this problem. I know that centre of circle is 5,0 and radius is 3 and the second eqn is a parabola..but that's about it so far..
any ideas?

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Oct 2, 2005

Tide

Science Advisor

Homework Helper

The center of the circle is (0, 5). I recommend making a sketch of the graphs and I think you'll find it quite illuminating! :)

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