The point of intersection of the pair of lines x²+xy+2y²-3x+2y+4=0 is

Correct Answer is : (2,−1)(2,-1)(2,−1)

Correct Answer is : (2,−1)(2,-1)(2,−1)

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AP EAMCET Engineering 21 Sep 2020 Shift 2 Paper

Section: Mathematics

Question : 32 of 160

Marks: +1, -0

x^2+xy+2y^2-3x+2y+4=0

Solution:

(d) The point of intersection of the pair of lines

f(x, y) \equiv x^{2}+x y+2 y^{2}-3 x+2 y+4=0

is same as the intersection of curve obtaining after partial differentiating of the curve W.r.t.

x

and

y

respectively.

\because \; \frac{\partial f}{\partial x}=2x+y-3=0 \; \dots \; \text{(i)}

\text{and} \; \frac{\partial f}{\partial y}=x+4y+2=0 \; \dots \; \text{(ii)}

By cross-multiplication method, we get

\frac{x}{2+12} = \frac{-y}{4+3} = \frac{1}{8-1}

⇒

(x, y)=(2,-1)

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