Where is the origin of a circle or what is it? Or how do you find it?
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Answers
Answer:
Thus, using the theorem of Pythagoras, x2 + y2 = r2 , and this is the equation of a circle of radius r whose centre is the origin O(0, 0). The equation of a circle of radius r and centre the origin is x2 + y2 = r2 .
Step-by-step explanation:
Finding the Equation of a Circle
Step 1: On a piece of graph paper, draw an x−y plane. Using a compass, draw a circle, centered at the origin that has a radius of 5. Find the point (3,4) on the circle and draw a right triangle with the radius as the hypotenuse.
Step 2: Using the length of each side of the right triangle, show that the Pythagorean Theorem is true.
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Step 3: Now, instead of using (3,4), change the point to (x,y) so that it represents any point on the circle. Using r to represent the radius, rewrite the Pythagorean Theorem.
The equation of a circle, centered at the origin, is x2+y2=r2, where r is the radius and (x,y) is any point on the circle.
Let's find the radius of x2+y2=16 and graph.
To find the radius, we can set 16=r2, making r=4. r is not -4 because it is a distance and distances are always positive. To graph the circle, start at the origin and go out 4 units in each direction and connect.
Now, let's find the equation of the circle with center at the origin and passes through (−7,−7).
Using the equation of the circle, we have: (−7)2+(−7)2=r2. Solve for r2.
(−7)2+(−7)249+4998=r2=r2=r2
So, the equation is x2+y2=98. The radius of the circle is r=98−−√=72–√.
Finally, let's determine if the point (9,−11) is on the circle x2+y2=225.
Substitute the point in for x and y and see if it equals 225.
92+(−11)281+121202=225=?225≠225
The point is not on the circle
Answer:
Thus, using the theorem of Pythagoras, x2 + y2 = r2 , and this is the equation of a circle of radius r whose centre is the origin O(0, 0). The equation of a circle of radius r and centre the origin is x2 + y2 = r2 .
Step-by-step explanation:
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