Sketch the circles y2 x2 1 and y2 x - 32 4 there is a

Question

Question: 1. Sketch the circles y² + x² = 1 and y² + (x - 3)² = 4. There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent line touches each circle.

2. If y = arcsin x then x = sin y. Use implicit differentiation on x = sin y to show that

(d/dx)arcsin x = 1/√(1 - x²)