Question

Determine the circle radius with the circle center ( 3 , 9 ) containing the point ( 8 , − 3 )

Answer 1

Explanation:

An equation of a circle with center (3,9)

whose radius is R :

(x-3)²+(y-9)²=R²

Substituting x=8, y=-3, we have :

5²+12²=R²

169=R²

13=R (∵R>0)

So the radius of the given circle is 13.

Just to remind you,

the equation of a circle is originated from Pythagoras theorem,

which represents the distance between

the center and an arbitrary point (of the circle).

Answer 2

First of all, (8,-3) is a point from the circle. Since, the center coordinates are also given, the distance between these two points would be the radius of the circle.

Distance formula: d=√((x_2-x_1)²+(y_2-y_1)²)

Step-to-step explanation:
Substitute the given coordinates into the formula

d=√((8-3)²+(-3-9)²)

d=√((5)²+(-12)²)

d=√(25+144)

d=√169

d= 13

Answer:
13