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First, we can see that this curve is a circle with a radius of √3 and a center point of [2, 3] by converting it to a more readable format. This is done by "completing the squares":
x2 + y2 - 4x - 6y + 10 = 0
∴(x2 - 4x + 4) + (y2 - 6y + 9) + 10 - 13 = 0
∴(x - 2)2 + (y - 3)2 = 3
So the curve at any point will be a simple arc.
Now, if by "what is the curvature ... at any point", you mean "what is the slope of the curve", then we would need to find the rate of change of y with respect to x. This is done by first solving for y and then taking it's derivative:
(x - 2)2 + (y - 3)2 = 3
∴(y - 3)2 = 3 - (x - 2)2
∴y - 3 = [3 - (x - 2)2]1/2
∴y = [3 - (x - 2)2]1/2 + 3
∴y = (3 - x2 + 4x - 4)1/2 + 3
∴y = (x2 + 4x - 1)1/2 + 3
We now have our curve solved for y, and we can take it's derivative with respect to x to find it's slope:
y = (x2 + 4x - 1)1/2 + 3
∴dy/dx = (1/2)(x2 + 4x - 1)-1/2(2x + 4)
∴dy/dx = (x + 2) / (x2 + 4x - 1)1/2
And to put it in proper form with radicals in the numerator:
dy/dx = (x + 2)(x2 + 4x - 1)1/2 / x2 + 4x - 1
What else can I help you with?
If xz plus zy equals xy and xz equals zy then the point z is?
mid point of xy
What is the common point of these equations x plus 2y equals 6 x plus y equals 2?
When x = -2 then y = 4 which is the common point of intersection of the two equations.
Which equation crosses the y axis at the highest point- y equals x plus 2 or y equals x plus 4?
The second
What is the point of intersection of the parabolas of y equals 3x squared plus 10x plus 11 and y equals 2 -2x -x squared?
They intersect at the point of: (-3/2, 11/4)
What is the common point of these equations x plus 2y equals 6 and x plus y equals 2?
x = -2 and y = 4 (-2,4)
If xz plus zy equals xy and xz equals zy then the point z is?
mid point of xy
What is the common point between x equals 2 and y equals 2x plus 1?
The point (4, 5) is.
What is the common point of these equations x plus 2y equals 6 x plus y equals 2?
When x = -2 then y = 4 which is the common point of intersection of the two equations.
If ac plus cb equals ab and ac equals cb then the point c is?
the midpoint of AB.
Which equation crosses the y axis at the highest point- y equals x plus 2 or y equals x plus 4?
The second
What is the point of intersection of the parabolas of y equals 3x squared plus 10x plus 11 and y equals 2 -2x -x squared?
They intersect at the point of: (-3/2, 11/4)
What is the common point of these equations x plus 2y equals 6 and x plus y equals 2?
x = -2 and y = 4 (-2,4)
What is the coordinates for y equals x y equals -x plus 2?
The coordinates of the point of intersection is (1,1).
What is the common point of these equations x equals 2 y equals 2x plus 1?
If X equals 2, then y = 5
If AC plus CB equals AB then point C is?
between A and B
What is the point of intersection if y equals x plus 1 and x equals -x plus 1x?
2
What is the point of intersection of the lines 5x plus 7y plus 29 equals 0 and 11x -3y -65 equals 0?
It works out that they intersect at: (4, -7)
