A point P(p,0) moves along the x-axis and a point Q lies on the curve y = x^2 such that PQ is vertical. The fixed point S is (2,0). Show that the area of triangle PQS, in square units, is A = \dfrac{1}{2}(2-p)p^2.

AM-1946

Connected rates of change

A Math · Secondary 4 · Hard · Connected rates of change

A point

P(p,0)

moves along the

x

-axis and a point

Q

lies on the curve

y = x^2

such that

PQ

is vertical. The fixed point

S

(2,0)

. Show that the area of triangle

PQS

, in square units, is

A = \dfrac{1}{2}(2-p)p^2

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