SOLUTION: express the length l of a chord of a circle of radius 5 as a function of its distance x from the centre of the circle, and determine the domain of the function
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Question 988668: express the length l of a chord of a circle of radius 5 as a function of its distance x from the centre of the circle, and determine the domain of the function Found 2 solutions by Boreal, solver91311:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! It helps to draw this.
The chord's length is twice the sqrt (25-x^2). The radius is the hypotenuse, the distance from the center and half the chord's length are the two legs.
y=2*sqrt(25-x^2)
domain of x is ([0,5].
At 0, we have the diameter, or 10.
At 5, we have a tangent to the circle and length 0.
Construct a radius to one endpoint of the chord. Construct another radius that intersects the chord at its midpoint. You should now have a right triangle, hypotenuse that measures (the radius of the circle), one leg that measures (the distance from the center of the circle to the chord), and the other leg that measures one-half of the measure of the chord length.
Use the Pythagorean Theorem to derive your function. The domain of the function will be
It is ok for to equal zero because the diameter of a circle is just a special case of a chord. However, cannot be equal to the radius of the circle because your can't have a chord of zero length.
John
My calculator said it, I believe it, that settles it
