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n200080 [17]
3 years ago
15

Write the equation in standard form. Identify the important features of the graph:

Mathematics
1 answer:
Lerok [7]3 years ago
6 0

Answer:

Standard form: \left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.

This equation represents the circle with the center at the point \left(\dfrac{9}{2},-5\right) and the radius r=\dfrac{11}{2}.

Step-by-step explanation:

Consider expression x^2+y^2-9x+10y+15=0.

First, form perfect squares:

(x^2-9x)+(y^2+10y)+15=0,\\ \\\left(x^2-9x+\dfrac{81}{4}\right)-\dfrac{81}{4}+(y^2+10y+25)-25+15=0,\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=10+\dfrac{81}{4},\\ \\\left(x-\dfrac{9}{2}\right)^2+(y+5)^2=\dfrac{121}{4}.

This equation represents the circle with the center at the point \left(\dfrac{9}{2},-5\right) and the radius r=\dfrac{11}{2}.

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