Answer:
d. ellipse; [tex]23\degree[/tex]
Step-by-step explanation:
The given equation is;
[tex]9x^2+4xy + 5y^2-40=0[/tex].
Comparing to the general equation;
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]
[tex]A=9,B=4,C=5[/tex]
[tex]\cot(2\theta)=\frac{9-5}{4}[/tex]
[tex]\cot(2\theta)=\frac{4}{4}[/tex]
[tex]\cot(2\theta)=1[/tex]
[tex]2\theta=\cot^{-1}[/tex]
[tex]2\theta=45\degree[/tex]
[tex]\theta=22.5\degree[/tex]
To the nearest degree is [tex]23\degree[/tex]
Since the coefficient of the [tex]x^2[/tex] is not equal to the coefficient of [tex]y^2[/tex] but the signs are the same, the conic is an ellipse.
