Question

prove that the general equation of the second degree is ax^2+2hxy+by^2+2gx+2fy=0 by rotating the axes through an angle θ
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Answer 1

Step-by-step explanation:

hlo mate here's your answer

Let the axes be rotated through an angleθ

so that

x → x cos θ − y sin θ

y → x sin θ + y cos θ

}

a(xcosθ−

ysinθ)

2

+

2h(xcosθ−

ysinθ)(xsinθ+

ycosθ)

+b(xsinθ+ ycosθ)

2

+ 2g(xcosθ− ysinθ)+ 2f(xsinθ+ ycosθ)+ c= 0

Collect the coefficients of xy and put it equal to zero

(−asin2θ+

bsin2θ)+

2h(cos

2

θ−

sin 2

0

cos 2 θ

sin 2 θ

=

a−b

2h

⇒

tan2θ=

a−b

2h

I hope its help you mark as brainlist