AP EAPCET 23-Aug-2021 Shift 1 Paper

Given, equation is 3x2+3y2+2xy=2 ...(i)
When coordinate axis are rotated through an angle θ , then
x=X‌cos‌θ−Y‌sin‌θ and y=X‌sin‌θ+Y‌cos‌θ
where, (X,Y) is new coordinate after transformation.
Given, θ=45° , then x=

x

√2

−

y

√2

and y=

x

√2

+

y

√2

Putting value of x and y in Eq. (i), we get
3(

X

√2

−

Y

√2

)2+3(

X

√2

+

Y

√2

)2 +2(

X

√2

−

Y

√2

)(

X

√2

+

Y

√2

)=2
⇒

3

2

(X−Y)2+

3

2

(X+Y)2+(X2−Y2)=2
⇒

3

2

[2X2+2Y2]+X2−Y2=2
⇒3X2+3Y2+X2−Y2=2
⇒4X2+2Y2=2
or 2X2+Y2=1
∴ Transformed equation is 2x2+y2=1