The Circle $$x^2 +y^2 -6x -10y+k =0$$ does not touch or intersect the coordinate axes and the point $(1,4)$ lies inside the circle,then the range of $K$ is ?
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1Welcome to Math.SE! I think you misunderstood a key aspect of this site. This is more about helping you find the right answer then giving you answers to arbitrary problems. For example, if you were to give us what you've tried, where you've looked, what you've read to answer the problem, and describe why you aren't satisfied/doubt what you've come across, I'm sure others would help. Also, choosing a descriptive title that described the content would help. For more, I recommend reading How to ask a good question? – davidlowryduda Sep 14 '17 at 14:21
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Can you put the equation into standard form for a circle $(x-a)^2+(y-b)^2=r^2?$ What does that tell you? – Ross Millikan Sep 14 '17 at 14:25
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the radius is a function of K now with the circle of center (3,5) – user479292 Sep 14 '17 at 14:29
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That is correct. You should edit it into your question. What is the function of $K$?. By the way, $k$ and $K$ are different variables. Please be consistent. – Ross Millikan Sep 14 '17 at 14:33
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my bad. the radius is √(34-k) only the small alphabet "k" just like in the equation of the circle. – user479292 Sep 14 '17 at 14:35