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Reptile [31]
3 years ago
13

Find a polar equation for the curve represented by the given cartesian equation. x2 + y2 = 10cx

Mathematics
2 answers:
RoseWind [281]3 years ago
6 0
The usual rectangular to polar substitutions can be used:
  x = r·cos(θ)
  y = r·sin(θ)

These give
  r² = 10c·r·cos(θ)
or
  r = 10c·cos(θ)

Anna11 [10]3 years ago
3 0

Answer:

The polar equation for the curve represented by the given cartesian equation is r=(10c)cos(\theta)

Step-by-step explanation:

<em>We were given the following equation</em>:

x^2+y^2=10cx

and the relations between cartesian and polar coordinates are given by

x=rcos(\theta)

y=rsin(\theta)

<em>where r is a radius and θ an angle</em>. Now we <u>replace this relations in the original cartesian equation</u>:

(rcos(\theta))^2+(rsin(\theta))^2=(10c)rcos(\theta)\Leftrightarrow r^2cos^2(\theta)+r^2sin^2(\theta)=(10cr)cos(\theta)\Leftrightarrow r^2(cos^2(\theta)+sin^2(\theta))=(10cr)cos(\theta)

and we use that

(cos^2(\theta)+sin^2(\theta))=1

to simplify, then

r^2=(10c)rcos(\theta)\Leftrightarrow r=(10c)cos(\theta)

wich <u>is the polar equation for the curve</u>.

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