MHB What is the equation of the circle tangent to the x-axis and with center (3, 5)?

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Circle
AI Thread Summary
The equation of the circle tangent to the x-axis with center at (3, 5) can be derived using the standard circle formula. The radius of the circle is equal to the y-coordinate of the center, which is 5, hence r = 5. Substituting the center coordinates into the equation results in (x - 3)² + (y - 5)² = 5². This simplifies to (x - 3)² + (y - 5)² = 25. Therefore, the final equation of the circle is (x - 3)² + (y - 5)² = 25.
mathdad
Messages
1,280
Reaction score
0
Find the equation of the circle tangent to the x-axis and with center (3, 5).

Can someone provide the steps needed to solve this problem?
 
Mathematics news on Phys.org
The equation of a circle centered ar $(h,k)$ is given by:

$$(x-h)^2+(y-k)^2=r^2$$

If the circle is tangent to the $x$-axis, then its radius must be $r=|k|\implies r^2=k^2$, thus we have:

$$(x-h)^2+(y-k)^2=k^2$$

We are given $(h,k)=(3,5)$, so plug in those numbers. :D
 
MarkFL said:
The equation of a circle centered ar $(h,k)$ is given by:

$$(x-h)^2+(y-k)^2=r^2$$

If the circle is tangent to the $x$-axis, then its radius must be $r=|k|\implies r^2=k^2$, thus we have:

$$(x-h)^2+(y-k)^2=k^2$$

We are given $(h,k)=(3,5)$, so plug in those numbers. :D

(x - h)^2 + (y - k)^2 = k^2

(x - 3)^2 + (y - 5)^2 = 5^2

(x - 3)^2 + (y - 5)^2 = 25
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

Similar threads

Replies
2
Views
3K
Replies
59
Views
2K
Replies
2
Views
1K
Replies
10
Views
3K
Replies
6
Views
1K
Replies
2
Views
1K
Replies
2
Views
2K
Back
Top