Question

If x^2+y^2 - 4x-6y+13=0 find the value of x:y​

Answer 1

Answer:

x:y = 2:3

I have attached the steps

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Answer 2

Given :

${x}^{2} + {y}^{2} - 4x - 6y + 13 = 0$

To find :

$x</u><u>:</u><u>y =</u><u> </u><u>?</u><u> </u><u>$

Solution :

${x}^{2} + {y}^{2} - 4x - 6y + 13 = 0 \\ \\ {x}^{2} + {y}^{2} - (2 \times x \times 2) - (2 \times y \times 3) + 4 + 9 = 0 \\ \\ </u><u>[</u><u> {x}^{2} - 2(x)(2) + {2}^{2} </u><u>]</u><u> + </u><u>[</u><u> {y}^{2} - 2(y)(3) + {3}^{2} </u><u>]</u><u> </u><u>= 0$

It is in the form :

${a}^{2} - 2ab + {b}^{2} = \: {(a - b)}^{2}$

we get ,,,,

${(x - 2)}^{2} + {(y - 3)}^{2} = 0 \\ \\ {(x - 2}^{2} = 0 \: \: \: and \: \: \: {(y - 3)}^{2} = 0 \\ x - 2 = \sqrt{0} \: \: \: and \: \: \: y - 3 = \sqrt{0} \\ x = 2 \: \: \: and \: \: \: y = 3$

Therefore ,,,,

x : y = 2 : 3

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