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Answer :

Using Distance formula, we have

\(\Rightarrow 10 = \sqrt{(2 -10)^2 + (-3-y)^2}\)

\(\Rightarrow 10 = \sqrt{(-8)^2 + 9 + y^2 + 6y}\)

\(\Rightarrow 10 = \sqrt{64 + 9 + y^2 + 6y}\)

Squaring both sides, we get

\(\Rightarrow 100 = 73 + y^2 + 6y\)

\(\Rightarrow y^2 + 6y + 27 = 0\)

Solving this Quadratic equation by factorization, we can write

\(\Rightarrow y^2 + 9y - 3y - 27 = 0\)

\( \Rightarrow y (y + 9) – 3 (y + 9) = 0\)

\(\Rightarrow (y + 9) (y - 3) = 0\)

\(\Rightarrow y = 3, -9\)

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