Geometry
# Area of Triangles

**Statement \(1\):** If the area of the triangle bounded by the lines \(y=x, x+y=8\) and the line through \(P=(h,k)\) parallel to the \(x\)-axis is \(4h^2,\) then \(P\) lies on either of the two lines represented by \(4x^2+8y-y^2-16=0.\)

**Statement \(2\):** The area of the triangle bounded by the lines \(y=x, x+y=8\) and the \(x\)-axis is equal to half of the area of the triangle bounded by the line \(x+y=8\) and the two coordinate axes.

Which of the following is true of the above two statements?

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