Please give detailed answers so I can see how these are supp

Please give detailed answers so I can see how these are supposed to be done. Find the rectangular equation that has the same graph as the given polar equation. Please do not do these if you do not know how!!!

a. 5sin2theta = 4

b. 7r = 14 tan theta

c. r = 6 + 5 sec theta

Solution

x/r=cos, y/r=sin

x²+y²=r²

a. 5sin2 = 4

5*2sincos = 4

5sincos = 2

5(y/r)(x/r)=2

5xy=2r²

5xy=2(x²+y²)

2x²+2y²-5xy=0

b. 7r = 14 tan theta

r =2(sin/cos)

r =2((y/r)/(x/r))

r =2(y/x)

(x²+y²) =2y/x

c. r = 6 + 5 sec theta

r = 6 + (5/cos)

r =6+(5/(x/r))

r =6+(5/x)r

r(1-(5/x))=6

r=6/(1-(5/x))

r =6x/(x-5)

(x²+y²) =6x/(x-5)