SOLUTION: The graph of the equation x^2 + y^2 + 8x − 10y − 40 = 0 is which of the following conic sections?
A. parabola
B. hyperbola
C. ellipse
D. circle
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Question 974686: The graph of the equation x^2 + y^2 + 8x − 10y − 40 = 0 is which of the following conic sections?
A. parabola
B. hyperbola
C. ellipse
D. circle
Found 2 solutions by Fombitz, htmentor:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
It's a circle centered at (-4,5) with a radius of 9.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
If we rearrange the equation, grouping the x and y terms, and move the constant term to the other side, we have:
x^2 + 8x + y^2 - 10y = 40
Complete the squares:
(1) (x+4)^2 = x^2 + 8x + 16
(2) (y-5)^2 = y^2 - 10y + 25
Since the constant terms add to 41, we need to subtract this from the LHS in order to write the equation as the sum of (1) and (2):
x^2 + 8x + y^2 - 10y -> (x+4)^2 + (y-5)^2 - 41 = 40 -> (x+4)^2 + (y-5)^2 = 81
This is the equation for a circle with center (-4,5), and radius sqrt(81) = 9
Graph is shown below.
Ans: D circle
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