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For what value of k does the equation x^2+10x+y^2+6y-k=0 represent a circle of radius 6?

Jun 25, 2020
edited by QuestionsBug  Jun 25, 2020

#1
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The question isn't complete :(

Jun 25, 2020
#2
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I seriously don't understand why so many people like to copy questions with latex...

where do they come from???

Jun 25, 2020
#3
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I don't know. Alcumus?

Please write out the question completely... I'll try to help when you do! :D

Jun 25, 2020
#4
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Yes, I actually got it from alcums, and I also fixed it, sorry.

QuestionsBug  Jun 25, 2020
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A circle equation is \((x-h)^2+(y-k)^2=r^2\), where (h, k) is the center and r is the radius.

We complete the square for x and y to get it in circle form.

Add 25 and 9 to both sides to complete the square.  \(x^2+10x+25+y^2+6y+9-k=25+9\)

Now we can write the squares. We also k to both sides. \((x+5)^2+(y+3)^2=34+k\)

It's in circle equation now!

Since the radius must be 6, 34+k=36.

k=2

Jun 25, 2020
#6
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Thank you so much! :)

QuestionsBug  Jun 25, 2020