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Answer :
The correct answer for the polar equation with an equivalent Cartesian equation is x2 + (y - 26)2 = 169.(option D)
To replace the polar equation r = 26 sin θ with an equivalent Cartesian equation, we can use the conversion formulas x = r cos θ and y = r sin θ. Substituting these into the given equation, we get:
x = 26 cos θ sin θ
y = 26 sin2 θ
Squaring and adding these equations, we can eliminate the trigonometric functions and obtain an equation in terms of x and y:
x2 + y2 = (26 cos θ sin θ)2 + (26 sin2 θ)2
x2 + y2 = 676 sin2 θ
x2 + y2 = 676 (y/26)2
Simplifying this equation, we get:
x2 + (y - 0)2/26 = 169
Therefore, the correct answer is D) x2 + (y - 26)2 = 169. This equation represents a circle centered at (0, 26) with a radius of 13, which is the distance from the origin to the point (0, 26) obtained by setting θ = π/2 in the polar equation. This is the equivalent Cartesian equation for the given polar equation, obtained by replacing the polar coordinates with their Cartesian equivalents.
Learn more on cartesian equations here:
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