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Integration by Substitution

If x2+y2-2x...

Question

If $x^{2} + y^{2} - 2 x + 6 y + 10 = 0,$ and x-3y=10, then the value of $x^{2} + y^{2}$ is

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Solution

The correct option is A 10
Given x-3y =10 multiply by two both sides then 2x-6y=20
$x^{2} + y^{2} - 2 x + 6 y + 10 = 0$
$\Rightarrow x^{2} + y^{2} - (2 x - 6 y) + 10 = 0$
$\Rightarrow x^{2}+y^{2}-(10)+10=0$
$\Rightarrow x^{2} + y^{2} - 20 + 10 = 0$
$\Rightarrow x^{2} + y^{2} = 10$

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