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Two pairs of straight lines $$x^2 — 7x + 6 = 0$$ and $$y^2 — 14y + 40 = 0$$ intersect to form a rectangle. Let the diagonals of the rectangle intersect at the point W. A circle with center W and with tangents as lines $$y^2 — 14y + 40 = 0$$ intersects lines $$x^2 — 7x + 6 = 0$$ at points P, Q, R, S. The area of the rectangle PQRS is
$$x^2 — 7x + 6 = 0$$ => x= 1, x=6$$PM\ =\sqrt{\ PW^2-MW^2}$$
$$y^2 — 14y + 40 = 0$$ => y= 4, y=10
$$W\ =\ \left(\frac{1+6}{2},\frac{4+10}{2}\right)\ =\ \left(\frac{7}{2},7\right)$$
QR = 6-1 =5
r = (10-4)/2 = 3
PW = r= 3
MW = QR/2 = 5/2
$$PM\ =\sqrt{\ PW^2-MW^2}$$ = $$\frac{\sqrt{\ 11}}{2}$$
PQ=2PM = $$\sqrt{\ 11}$$
Area of PQRS = QR x PQ = $$5\sqrt{\ 11}$$
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