Whats the radius and center of (x+4)^2+(y-2)^2=9
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Answer:
Step-by-step explanation:
Given :
Solution:
Thus ,
Thus the solution is irrational since square root 7 does not have a perfect square and equal to 6+2square root of 14
Given that 
, then 
The slope of a tangent line in the polar coordinate is given by:
Thus, we have:
Part A:
For horizontal tangent lines, m = 0.
Thus, we have:
Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,
Thus, we have:
</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
The slope of a tangent line in the polar coordinate is given by:
Thus, we have:
Part A:
For horizontal tangent lines, m = 0.
Thus, we have:
Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,
Thus, we have:
</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>