Question

write the equation of the circle with center (-3,2) and (6,4) a point on the circle

Answer 1

(x + 3)² + (y - 2)² = 85

the equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a, b ) are the coordinates of the centre and r is the radius

the radius is the distance from the centre to the point (6, 4 ) on the circle

r = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (6, 4 )

r = √(6 + 3 )² + (4 - 2 )² = √(81 + 4 ) = √85 ⇒ r² = 85

(x + 3)² + (y - 2)² = 85 ← equation of circle

Answer 2

Step-by-step explanation:

Prerequisites:

You need to know:

The distance formula

The standard equation of a circle.

Distance formula:

d = $\sqrt{(X_2-X_1)^2+(Y_2 - Y_1)^2}$

The standard equation of a circle

$(x - h)^2 + (y - k)^2 = r^2$

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First, use the standard equation of the circle and plugin the information we know.

We know the center is (h, k) = (-3, 2)

h = -3

k = 2

$(x - h)^2 + (y - k)^2 = r^2$

$(x - (-3))^2 + (y - 2)^2 = r^2$

$(x + 3)^2 + (y - 2)^2 = r^2$

Since we do not know our r value, we need to find r. We can find this value by using the distance formula. Remember, the radius (r) is the distance from the center of the circle to a point on the circle. Points we will use are (-3,2) (6,4)

$d = \sqrt{(X_2-X_1)^2 + (Y_2 - Y_1)^2}$

$d = \sqrt{(-3 - 6)^2 + (2 - 4)^2}$

$d = \sqrt{(-9)^2 + (-2)^2}$

$d = \sqrt{81 + 4}$

$d = \sqrt{85} = 9.21954457$

Now we plugin 9.21954457  for r.

$(x + 3)^2 + (y - 2)^2 = r^2$

$(x + 3)^2 + (y - 2)^2 = 9.21954457^2$

$(x + 3)^2 + (y - 2)^2 = 84.9999999$

Answer:

$(x + 3)^2 + (y - 2)^2 = 84.99999999$

OR

$(x + 3)^2 + (y - 2)^2 = 85$