AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

(d) The point of intersection of the pair of lines f(x,y)≡x2+xy+2y2−3x+2y+4=0 is same as the intersection of curve obtaining after partial differentiating of the curve W.r.t. x and y respectively.
∵‌‌‌

∂f

∂x

=2x+y−3=0‌...‌ (i) ‌
‌ and ‌‌‌‌

∂f

∂y

=x+4y+2=0‌...‌ (ii) ‌
By cross-multiplication method, we get
‌

x

2+12

=‌

−y

4+3

=‌

1

8−1

⇒ ‌‌(x,y)=(2,−1)