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Which conic section is represented by the equation shown below?

x² + y²8x-10y+10=0
OA. Ellipse
B. Hyperbola
C. Circle
OD. Parabola

User Suugaku
by
8.3k points

1 Answer

3 votes
To determine the conic section represented by the given equation, we can analyze the coefficients of the x², y², and xy terms.

The given equation can be rewritten as:

x² + y² - 8x - 10y = -10

Completing the square for x and y, we get:

(x - 4)² - 16 + (y - 5)² - 25 = -10

(x - 4)² + (y - 5)² = 31

Comparing this equation to the standard forms of the conic sections, we can see that it is the equation of a circle with center (4, 5) and radius √31.

Therefore, the answer is (C) Circle
User Ameo
by
7.6k points
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