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

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The discussion focuses on solving the system of equations defined by the circle equation x² + (y - 5)² = 9 and the parabola equation y = x² + K. The center of the circle is established at (0, 5) with a radius of 3. For K > 0, the conditions for the system to have 4 solutions or no solutions are determined by the intersection points of the circle and the parabola. A graphical sketch is recommended for better visualization of the solutions.

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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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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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