Question

Find the radius of a circle using the Pythagorean theorem, given that the center is at (3, 4) and the point (5, 6) lies on the circle.

Answer 1

Answer:

here is your answer

Step-by-step explanation:

The radius of your circle is the distance between the points (−1,4) and (3,−2). Using the Distance Formula:

D=(3−(−1))2+(−2−4)2−−−−−−−−−−−−−−−−−−−√=42+(−6)2−−−−−−−−−√=16+36−−−−−−√=52−−√.

What is the equation of the circle?

It is important to realize the "equation of the circle" is: a point (x,y) is on the circle if and only if the coordinates of the point x and y satisfy the equation. So, how to get the equation? What is the relationship between the x and y coordinates of a point on the circle?

Well, let (x,y) be a point on the circle. The big idea is:

The distance from the point (x,y) to the center (−1,4) is 52−−√.

So, using the distance formula (with (x2,y2)=(x,y) and (x1,y1)=(−1,4)) , it follows that

52−−√=(x−(−1))2+(y−4)2−−−−−−−−−−−−−−−−−−√.

hope u understood

plzz mark me as brainliest plzz

Answer 2

Answer:

The radius of the circle is $2\sqrt{2}$ units.

Step-by-step explanation:

Step 1 of 2

• Draw a circle taking the point (3, 4) as a center. Mark the center as O.
• It is given that the point (5, 6) lies on the circle. Mark the point (5, 6) as A.
• Join O to A.
• Now, draw the lines from the points A and O. Mark their point of intersection point as B.
• Thus, the ΔOAB is a right-angled triangle.

Step 2 of 2

Find the radius of the circle, i.e., the length of OA.

In ΔOAB,

Using the Pythagoras theorem,

$OA^2=AB^2+OB^2$

$OA^2=2^2+2^2$

$OA^2=4+4$

$OA^2=8$

$OA =\sqrt{8}$

$OA = 2\sqrt{2}$

Final answer: The radius of the circle is $2\sqrt{2}$ units.

#SPJ2