Question

13.
The equation 3x2 + 2xy + 3y2 – 18x - 22y + 50 = 0 is
transformed to 4x2 +2y2 =1 when referred to the rectangular axes
through the point (2, 3). Find the inclination of the latter axes to the former.
​

Answer 1

Step-by-step explanation:

When axes are rotated through 45

0

,

x=xcosθ−ysinθ=

2

x−y

y=xsinθ−ycosθ=

2

x+y

3x

2

+3y

2

+2xy=2⇒3(

2

x−y

)

2

+3(

2

x+y

)

2

+2(

2

x

2

−y

2

)=2

3(x

2

+y

2

−2xy)+3(x

2

+y

2

+2xy)+2x

2

−2y

2

=4

4(2x

2

+y

2

)=4

⇒2x

2

+y

2

=1