Convert this into a polar equation:

Question

((x^2)/4)+((y^2)/49)=1?

Answer 1

The relation between rectangular coordinates and polar system as follows :

x = r cos(θ), y = r sin(θ) and r² = x² + y².

(x²/4) + (y²/49) = 1.

[(r cos θ)²/4] + [(r sin θ)²/49] = 1

[ 49(r² cos² θ)+ 4(r² sin² θ) ]/196 = 1

49r² cos² θ+ 4r² sin² θ = 196

r²(49cos² θ+ 4sin² θ) = 196

r² = 196/(49cos² θ+ 4sin² θ)

 r = ±√[ 196/(49cos² θ+ 4sin² θ) ]

⇒ r = ±14/√(49cos² θ+ 4sin² θ).