SOLUTION: An engineer determines that the shape of a mirror surface in a motion sensor can be described by the equation 9x^2 – 25y^2 – 12x + 20y = 26. Identify the conic section that represe

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Question 1087179: An engineer determines that the shape of a mirror surface in a motion sensor can be described by the equation 9x^2 – 25y^2 – 12x + 20y = 26. Identify the conic section that represents the shape of the mirror.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
write in standard form:
9x%5E2-25y%5E2+-12x+%2B+20y+=+26.....complete squares
9x%5E2++-12x+-25y%5E2%2B+20y+=+26
%289x%5E2++-12x+%29-%2825y%5E2-20y+%29=+26
9%28x%5E2++-%2812%2F9%29x+%29-25%28y%5E2-+%2820%2F25%29y+%29=+26
9%28x%5E2++-%284%2F3%29x%2Bb%5E2+%29+-9b%5E2-25%28y%5E2-%284%2F5%29y%2Bb%5E2+%29-25b%5E2=+26

9%28x++-2%2F3%29%5E2++-9%284%2F9%29-25%28y-+2%2F5%29%5E2+-25+%284%2F25%29=+26
9%28x++-2%2F3%29%5E2++-4-25%28y-+2%2F5%29%5E2+-4=+26
9%28x++-2%2F3%29%5E2++-25%28y-+2%2F5%29%5E2+=+26%2B8
9%28x++-2%2F3%29%5E2++-25%28y-+2%2F5%29%5E2+=+34
%289%2F34%29%28x++-2%2F3%29%5E2++-%2825%2F34%29%28y-+2%2F5%29%5E2+=1=> hyperbola represents the shape of the mirror





Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

An engineer determines that the shape of a mirror surface in a motion sensor can be described by the equation 9x^2 – 25y^2 – 12x + 20y = 26. Identify the conic section that represents the shape of the mirror.
As the leading coefficients (2nd degree) are different (could also be the SAME), and as they have DIFFERENT signs, the mirror is in the shape of a highlight_green%28HYPERBOLA%29