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saul85 [17]
3 years ago
7

Find a polar equation of the form r2=f(θ) for the curve represented by the cartesian equation x2−y2=1. (note the power of r in t

he equation!)
Mathematics
1 answer:
iragen [17]3 years ago
4 0
The equations to transform from Cartesian to polar :
x = r cos θ   , y = r sin θ
Or
x² = r² cos² θ   , y² = r² sin² θ

To <span>represent the Cartesian equation x²−y²=1
substitute with the values of </span><span>x² and y²
</span>
∴ r² cos² θ - r² sin² θ = 1
   r² (cos² θ - sin² θ) = 1
but cos² θ - sin² θ = cos 2θ
∴ r² cos 2θ = 1
   r² = 1/cos 2θ

∴ r² = sec 2θ  ⇒⇒⇒⇒ The required equation







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