Question

**1.Write each equation in the x'y'-plane for the given value of θ. Then identify the**

** conic.**

**5x**²**+6y**²**=30; θ** **=30**°

a-5(x')²＋x'y'＋6(y')² - 30=0; ellipse

b-21(x')² - 23(y') - 120=0: hyperbola

c-21(x')² ＋2√3x'y'＋23(y')² - 120=0; ellipse

d-21(x') - 2√3x'y' - 23(y')² - 120=0; ellipse

**2.Write an equation for each conic in the xy-plane for the given equation in x'y' form and the given value of θ.**

**(x')²=16(y'); θ =45°**

a-x² + 16xy + y²=0

b-x² + 16√2x + 2xy - 16√2y + y²=0

c-x² - 16√2x - 2xy - 16√2y - y²=0

d-x² + 2xy + y²=0

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