Question

5. (a) Give an equation in polar coordinates that represents the circle below y 4 4 6 (b) Find the area contained within the circle given in part (a) by using the definite integral for area in polar coordinates Use the definition of the derivitive in polar coordinates to find the points, (,0), on the circle where vertical tangent lines exist

Answer 1

G 2 (Veloso, ys1200 2 4 - Centre at Coo) circle ond io 2 radius of So equation of Circh LI MzYcuso x² + y² = 2² iy= zrsno r2(con otsin²o) = 2 ² r² = 2² given >> In polur 1r 22 ( equation afterche b is giun by the In polar cardinete ara 02 rerz A 2 1 rdr do Oza rzrl Circle have so we for gien 21 217 a dQ Az rardy 020 u Az = ) z UR (A2415 ar X GW /

know that we stope dy dk 2 In polar cordinate of jongent line is giun by, :'(o) sino + flo).000 f(0) 100 MO) SRO ) flolan 2) d (0)20 2 r = 2 I costo con lo Sno 2 dy तर have, ovira + cool oxcayo - 2sin o So for urtical tangent line we sino =0 0 =0 2 polar point line cut we 2 heu usticul tingent (-2,0), (2,7)