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Rewrite the following rectangular equation in polar form assuming a is a real constant.x2 + y2 = 11a=

Rewrite The Following Rectangular Equation In Polar Form Assuming A Is A Real Constantx2 Y2 11a class=

Sagot :

Answer:

The polar form is

r = √11a

Explanation:

The given equation is

x^2 + y^2 = 11a

Recall,

x = rcosθ

y = rsinθ

By substituting these values into the equation, we have

(rcosθ )^2 + ( rsinθ)^2 = 11a

r^2cos^2θ + r^2sin^2θ = 11a

r^2cos^2θ + r^2sin^2θ - 11a = 0

By factorizing r^2, we have

r^2(cos^2θ + sin^2θ) = 11a

Recall, cos^2θ + sin^2θ = 1

Thus, we have

r^2 = 11a

Taking the square root of both sides,

r = √11a

The polar form is

r = √11a

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