The equation 8 x^2-24 x y+18 y^2-6 x+9 y-5=0 | vedclass

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(B) The given equation is $8 x^2-24 x y+18 y^2-6 x+9 y-5=0$.This can be rewritten as $(2 \sqrt{2} x - 3 \sqrt{2} y)^2 - 3(2 x - 3 y) - 5 = 0$.Let $2 x

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pair of parallel lines

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(B) The given equation is $8 x^2-24 x y+18 y^2-6 x+9 y-5=0$.This can be rewritten as $(2 \sqrt{2} x - 3 \sqrt{2} y)^2 - 3(2 x - 3 y) - 5 = 0$.Let $2 x - 3 y = t$. Then the equation becomes $2(2 x - 3 y)^2 - 3(2 x - 3 y) - 5 = 0$.Substituting $t = 2 x - 3 y$,we get $2 t^2 - 3 t - 5 = 0$.Factoring the quadratic: $2 t^2 - 5 t + 2 t - 5 = 0 \implies t(2 t - 5) + 1(2 t - 5) = 0$.So,$(t + 1)(2 t - 5) = 0$.This gives $t = -1$ or $t = 5/2$.Substituting back $t = 2 x - 3 y$,we get $2 x - 3 y + 1 = 0$ and $2 x - 3 y - 5/2 = 0$,which is $4 x - 6 y - 5 = 0$.Since the slopes of both lines are $m = 2/3$,the lines are parallel.

The equation $8 x^2-24 x y+18 y^2-6 x+9 y-5=0$ represents a

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