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

(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: i literally just answered this question but they want me to do it again

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true