Question

If a variable circle having centre P(α, β), β > 0 always touching the circle x² + (y - 1)²  = 1 and x-axis, then the area bounded between locus of P and y = 4 is __.

Answer 1

From the condition, C₁C₂ = r₁ + r₂

Shaded area is \(\frac23\) of corresponding rectangle

\(= \frac23 \times 8 \times 4\)

\(= \frac{64}3\)

\(= 11.33\)