A circle centered at the origin runs through the point (-6, 8). What is the radius of the circle?
2007-03-29 06:53:34 · 8 answers · asked by JoAnna 2 in Science & Mathematics ➔ Mathematics
10. Your best bet is to just dump (0,0) and (-6,8) into the distance formula since the radius of a circle is defined as the distance between the center and any point on the circle. This is:
D = sqrt [ (x1 - x2)² + (y1 - y2)²]
= sqrt [ (-6 - 0)² + (8-0)² ]
= sqrt 100
= 10
The equation of the circle is:
x² + y² = 100
2007-03-29 07:00:36 · answer #1 · answered by Kathleen K 7 · 1⤊ 0⤋
We need to find the distance between the origin and the point (-6,8). We can set up a triangle within the circle and use the Pythagorean Theorem to solve this one. We would have a triangle that is 8 units tall and 6 units across. Using the Pythagorean Theorem,
a^2 + b^2 = c^2, or
64 + 36 = c^2
100 = c^2
10 = c
The hypotenuse here is 10 units long and therefore the circle must have a radius of 10 units.
2007-03-29 07:09:33 · answer #2 · answered by Ohioguy95 6 · 0⤊ 0⤋
Look at it as a right triangle with short sides that are 6 units and 8 units long respectively. Then pythagoras tells us that the hypotenuse (radius) is the square root of 36+64, or 10 units.
2007-03-29 07:01:40 · answer #3 · answered by indiana_jones_andthelastcrusade 3 · 0⤊ 0⤋
The eqn of circle in standard form is
(x-a)^2 + (y-b)^2 = r^2
where (a,b) is centre and r is radius
in this case (a,b) = (0,0)
so eqn becomes
x^2+y^2 = r^2
we know one point (x,y) = (-6,8)
=> r^2 = 6^2 + 8^2 = 100 => r = 10
ANswer radius = 10
ANd equation of circle => x^2+y^2 = 100
2007-03-29 07:00:09 · answer #4 · answered by Nishit V 3 · 1⤊ 0⤋
First, i anticipate the polygon is established with n aspects. The inscribed radius is often called the "apothem", at the same time as the circumscribed radius is only the "radius". i visit apply "a" to talk with the apothem length and "r" for the radius. the attitude between the radius and the apothem is ?/n. The apothem makes a suitable attitude with the aspect, so the apothem and radius form a suitable triangle with the aspect. we can see that cos(?/n) = a / r and it is a complication-free formulation in words of purely n pertaining to both lengths.
2016-12-02 23:40:36 · answer #5 · answered by Anonymous · 0⤊ 0⤋
x² + y² = r²
36 + 64 = r²
r² = 100
r = 10
2007-03-29 07:02:46 · answer #6 · answered by Como 7 · 0⤊ 0⤋
O(0,0) and A(-6,8),,,,OA=sqrt[ (-6-0)^2+(8-0)^2=sqrt[36+64]=
OA=sqrt[100]
OA=10 or radius=r=OA=10
2007-03-29 08:03:40 · answer #7 · answered by Anonymous · 0⤊ 0⤋
sq. rt. (6^2+8^2) = 10
2007-03-29 07:00:43 · answer #8 · answered by jw72135 3 · 1⤊ 0⤋