Solve the given Alternate Coordinate Systems and give a correct answer10) Convert the equation from Cartesian to polar coordinates solving for r^2: frac{x^2}{9} - frac{y^2}{16} = 25

Falak Kinney 2021-01-02 Answered

Solve the given Alternate Coordinate Systems and give a correct answer 10) Convert the equation from Cartesian to polar coordinates solving for r2:
x29y216=25

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Expert Answer

BleabyinfibiaG
Answered 2021-01-03 Author has 118 answers

Solution: Relation between polar Co-ordinate system and Cartesian Co-ordinate system x=rcos0y=rsin0

r=x2+y2

given that - x29y216=25 put x=rcos0, y=esin0
r2cos200r2sin2016=25
r2[16cos209sin20177]=25
r2=25×177[(7cos)2(3sin)2][a2h2=(ab)(a+b)]
r2=25×177(7cos03sin0)(4cos0+3sin0)
r2=25×1775[(75cos035sin0)]5[(75cos0+35sin0)]
r2177(75cos035sin0)(75cos0+35sin0)[sin(53)=35]
r2=177(sin53cos0cos53sin0)(sin53cos0+cos53sin0)  formula 

sin(A+B)=sinAcosB+cosAsinB

sin(AB)=sinAcosBcosAsinB

r2177[sin(530)][sin(53+0)]

r2=177[sin(530)][sin(0+53)]

Finally answer is r2=177[sin(530)][sin(0+53)]

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