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Convert the polar equation to the Cartesian equation

  • #1
251
11

Homework Statement


Replace the polar equation with an equivalent Cartesian equation.

##r^2 = 26r cos θ - 6r sin θ - 9##
a)##(x - 13)^2 + (y + 3)^2 = 9##
b)##(x + 26)^2 + (y - 6)^2 = 9##
c)##26x - 6y = 9##
d)##(x - 13)^2 + (y + 3)^2 = 169##

Homework Equations


##x= r cos \theta##
##y= r sin \theta##
##x^2+y^2 = r^2##

The Attempt at a Solution


##r^2 = 26r cos θ - 6r sin θ - 9##
##x^2 + y^2 = 26 x - 6 y -9 ##
##x^2 -26x + y^2 + 6 y = -9 ##
##(x-13)^2 - 169 + ( y+3 )^2 -9 = -9##
##(x-13)^2 + (y+3)^2 = 169 ##
The answer is (d) . Right ?
 

Answers and Replies

  • #2
34,074
9,975
Looks good.
 

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