Question

Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation
7
x
2
+
24
x
y
−
34
x
+
24
y
−
185
=
0

Answer 1

$7x^2+24xy-34x+24y-185=0$

The general equation of line 2 order:

$a_{11}x^2+2a_{12}xy+a_{22}y^2+2a_{1}x+2a_2y+a=0$

The acute angle of rotation eliminates the product term from the equation 

$\tan2\alpha=\frac{2a_{12}}{a_{11}-a_{22}}$

In our case

$a_{11}=7, 2a_{12}=24, a_{22}=0$

$\tan2\alpha=\frac{24}{7-0}=\frac{24}{7}=3.43\\ 2\alpha=74^0\\ \alpha=37^0$