Asked by Lucy
For the quadratic surface defined by 36x^2-72x-9y^2-36y-16z^2+96z-288=0
Put the surface into standard form and identify the center of the surface
Put the surface into standard form and identify the center of the surface
Answers
Answered by
Reiny
complete the square ...
36(x^2 - 2x + ...) - 9(y^2 + 4y + ....) - 16(z^2 - 6z + ...) = 288
36(x^2 - 2x + 1) - 9(y^2 + 4y + 4) - 16(z^2 - 6z + 9) = 288 + 36 - 36 -144
36(x-1)^2 - 9(y+2)^2 - 16(z-3)^2 = 144
divide by 144
(x-1)^2 /4 - (y+2)^2 /16 - (z+3)^2 /9 = 1
centre is (1,-2,-3)
36(x^2 - 2x + ...) - 9(y^2 + 4y + ....) - 16(z^2 - 6z + ...) = 288
36(x^2 - 2x + 1) - 9(y^2 + 4y + 4) - 16(z^2 - 6z + 9) = 288 + 36 - 36 -144
36(x-1)^2 - 9(y+2)^2 - 16(z-3)^2 = 144
divide by 144
(x-1)^2 /4 - (y+2)^2 /16 - (z+3)^2 /9 = 1
centre is (1,-2,-3)
Answered by
Lucy
So this is a hyperboloid of 2 sheets right?? Thanks so much!
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