My Math Forum Circle Intersecting Axis

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 June 3rd, 2013, 05:22 AM #1 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Circle Intersecting Axis Based on the y-intercepts I've found, adding them together would yield the correct answer, but this is not the difference between the values and, hence, not the length of the intercept. Can anyone help? Many thanks. Q. K is the circle $x^2+y^2-4x-8y-5=0$. Find the length of the intercept the circle cuts off the y-axis. Attempt: Let $x=0:\,\,y^2-8y-5=0$ Apply quadratic equation: $\frac{-(-+/-\sqrt{(-^2-4(1)(-5)}}{2(1)}=\frac{8+/-\sqrt{64+20}}{2}=\frac{8+/-\sqrt{84}}{2}=4+/-\sqrt{21}" /> Difference between y intercepts = length of intercept: $4+\sqrt{21}-(4-\sqrt{21})=2\sqrt{21}$ Ans. (From text book): 8
 June 3rd, 2013, 06:12 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Circle Intersecting Axis I agree with your interpretation and result.
 June 3rd, 2013, 06:22 AM #3 Senior Member   Joined: Sep 2011 Posts: 395 Thanks: 0 Re: Circle Intersecting Axis Great! Thank you very much.

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