Give the center and radius of the circle represented by each equa...

Question

Give the center and radius of the circle represented by each equation. See Examples 3 and 4. x^2+y^2+6x+8y+9=0

Accepted Answer

While the circle described by the following equation identified the center in radius, our equations X squared plus Y squared plus 18 X plus 26 Y plus 1 50 is equals to zero. Now, to solve this, you wanna write this circle equation in standard form. Standard form of a circle is X minus H squared plus Y minus K squared. As equals to R squared. I'm gonna take our equation and group together our XS and our Ys X squared plus 18 X plus Y squared Plus 26 Y S equals to negative 150 moving our 150 over to the right side. Now, we want to change this equation into our standard form to do that. We will complete the square for both of our polynomials. Here we have X square plus 18 X first to complete the square. We will take The B of Our Quadratic R 18, Add on to the end 18 divided by two squared. Well, then do the same for the wet Y squared plus 26 Y plus 26 divided by two squared. Like so That's equal to -150. On the right side, we add 18 divided by two squared and add divided by two squares like so we can then simplify here for the X, we get X squared plus 18, X plus 81. The Y you can Y squared plus 26 Y Plus 169 set equals To negative 1 50 plus 81 plus 1 69. We can simplify this even further. We can factor our X squared plus 18 and X plus and two X plus nine squared. Fact, our weiss To y plus squared on the right side, the whole thing will be equals to 100. Now, you know the sinner is H K, If we look at our equation, our H will be negative nine RK will be negative Radius or R. Squared is 100. That means our R will be equals to 10. We then have our radius and our center which corresponds to answer A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Give the center and radius of the circle represented by each equation. See Examples 3 and 4. x^2+y^2+6x+8y+9=0

Key Concepts

Standard Form of a Circle

Completing the Square

Quadratic Terms

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