These curves are circles which intersect at the origin and at (122a,4). At the origin, the first circle has a horizontal tangent and the second a vertical one, so the tangents are perpendicular here. For the first circle [r=asin],dyd=acossin asincos=asin2=a at =4 and dxd=acos2-asin2=acos2=0 at =4, so the tangent here is vertical. Similarly, for the second circle ]=[acos and dxd=-asin2=-a at =4, so the tangent is horizontal, and again the tangents are perpendicular.