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The area of the triangle formed by intersection of a line parallel to x – axis and passing through P(h,k) with the lines $y = x a n d x + y = 2 i s 4 h^{2}$ . The locus of P is

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$y = 2 x \pm 1$

$\begin{array}{l} y = \pm 2 x + 1 \end{array}$

$\begin{array}{l} y = 3 x \pm 2 \end{array}$

$\begin{array}{l} y = \pm 3 x - 2 \end{array}$

answer is C.

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Detailed Solution

$\begin{array}{l} \begin{array}{l} y = x, x + y = z, y = k \\ (1, 1) (2 - k, k) (k, k) \\ A r e a o f Δ A B C = 4 h^{2} \end{array} \\ \frac{1}{2} | \begin{array}{l} 1 1 1 \\ 2 - k k 1 \\ k k 1 \end{array} | = 4 h^{2} \end{array}$

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