need help finding missing coordinate: circle w/ eqn x^2+y^2=100, chord at (0,-10),...

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Glyndon

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Hello everyone. I am having problems with this question. Any help would be appreciated.

A circle has equation x2 + y2 = 100 and a chord at (0, -10), (6, h)
Need to find the value of h.

I know I must be missing something basic but cannot figure it out.

thanks in advance.
 
Glyndon said:
Hi everyone,

Am trying to figure out this problem.

A circle has equation x2 + y2 = 100, there is a chord with coordinates (0, -10) and (6, h).

What is the value of h?

Any help would be appreciated.
Click to expand...
Where is the center of the circle?

What is the diameter of the circle?

Make an approximate sketch and use Pythagorean theorem.
 
Glyndon said:
A circle has equation x2 + y2 = 100 and a chord at (0, -10), (6, h)

Need to find the value of h.
Click to expand...
In this exercise, there are two such chords.

If they did not specify which one they're talking about, then I suppose you ought to report both values of h.


I know I must be missing something basic but cannot figure it out.
Click to expand...
Maybe it's this: If a point is at one end of a chord, then it must lie on the circle.

In other words, the coordinates (6, h) must satisfy the circle's equation.

Substitute these coordinates in x^2+y^2=100, and solve for h. :cool:
 
Denis said:
Hmmm...the standard circle equation is:

(x - h)^2 + (y - k)^2 = [100]

Wonder if the given (6,h) should be (h,6).
Click to expand...
That interpretation of h -- along with endpoint (0,-10) -- would make the exercise more interesting, but solving for (h,k) would still result in two possible chords.

(Four solutions for h, actually, but two of them are imaginary.) :cool:
 
(6, 8) and (6,-8) are on the circle

Note that (x,y)=(6, 8) solves xx+yy=100
Note that (x,y)=(6,-8) solves xx+yy=100

What is the distance between (6, 8) and (0,-10)?
What is the distance between (6,-8) and (0,-10)?
 
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