Need help please:
(3,0) (7,6)
(x-7)2 + (y-6)2 = 7(2)
(x-7)2 + (y-6)2 = 49
Having difficulty with this problem.Can someone help?
You don't say what the actual problem is.
I see the resemblance to finding the equation of a circle??
What are you trying to find?
It says to write an equation of a circle with diameter
__
AB
Of course! I'd be happy to help you.
It seems like you have been given two points, (3,0) and (7,6), and a set of equations involving variables x and y. The equations appear to be standard form equations for circles.
To analyze this further, let's break it down and go step by step:
1. The equations (x-7)² + (y-6)² = 7² and (x-7)² + (y-6)² = 49 are both in the form of (x-a)² + (y-b)² = r², which represents a circle with center (a, b) and radius r.
2. Looking at the first equation, (x-7)² + (y-6)² = 7², we can see that the center of the circle is at coordinates (7, 6) and the radius is 7, since 7² equals 49.
3. Let's verify if the given points, (3,0) and (7,6), lie on this circle. To do this, we can substitute the x and y values of each point into the equation and see if they satisfy the equation.
For the point (3,0):
(3-7)² + (0-6)² = 16 + 36 = 52, which is not equal to 49. Therefore, (3,0) does not lie on the circle described by the equation.
For the point (7,6):
(7-7)² + (6-6)² = 0 + 0 = 0, which is equal to 49. Therefore, (7,6) does lie on the circle described by the equation.
4. Now, let's move on to the second equation, (x-7)² + (y-6)² = 49. We can see that the center of this circle is also at coordinates (7, 6), but the radius is now the square root of 49, which is 7.
5. Similar to the first equation, we can verify if the given points, (3,0) and (7,6), lie on this second circle. By substituting the x and y values, we can see that both points satisfy the equation and lie on the circle.
So, to summarize, the point (3,0) does not lie on the first circle, but it does lie on the second circle. The point (7,6) lies on both circles.
I hope this explanation assists you in understanding how to analyze circles described by standard form equations. Let me know if there is anything else I can help with!