Question

Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form.

97x^2 + 130xy + 97y^2 - 2592 = 0

Answer 1

97x² + 130xy + 97y² - 2592 = 0
cot(2θ) = (97-97)/130 ... ⇒ θ = π/4
x = X cos(θ) - Y sin(θ) and y = X sin(θ) + Y cos(θ)
97/2 (X - Y)² + 65 (X - Y)(X + Y) + 97/2 (X + Y)² - 2592 = 0
162 X² + 32 Y² = 2592
X²/16 + Y²/81 = 1

Answer: X²/16 + Y²/81 = 1

Answer 2

@ziko1995 can you help me with these too?

x2 + 10xy + y2 - 8 = 0

145x2 - 34xy + 145y2 - 10368 = 0

Answer 3

x² + 10xy + y² - 8 = 0
cot(2θ) = (1-1)/10 ... ⇒ θ = π/4
1/2 (X - Y)² + 5 (X - Y)(X + Y) + 1/2 (X + Y)² - 8 = 0
3 X² - 2 Y² = 4
X²/(4/3) - Y²/2 = 1

Answer: X²/(4/3) - Y²/2 = 1

145x² - 34xy + 145y² - 10368 = 0
cot(2θ) = (145-145)/-34 ... ⇒ θ = π/4
145/2 (X - Y)² - 17 (X - Y)(X + Y) + 145/2 (X + Y)² - 10368 = 0
128 X² + 162 Y² = 10368
X²/81 + Y²/64 = 1

Answer: X²/81 + Y²/64 = 1

Answer 4

wow thanks!

Answer 5

:D

Answer 6

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Answer 7

alright, i cant go on facebook, twitter, etc from this computer but i will later