Question

The equation of circle having a diameter with endpoints (-3, 1) and (5, 7) is
(x - 4)² + (y - 3)² = 25
(x - 1)² + (y - 4)² = 25
(x - 1)² + (y - 4)² = 100

Answer 1

First, you need to find the mid point (center of the circle) using the mid point formula.

Then, you need to find the radius by using the distance formula from the midpoint to any endpoint of the given diameter.

Answer 2

d² = (1 + 3)² + (-3 - 7)²


d² = 16 + 100 = 116


diameter is √116 = 2.√29

Radius r = d/2 = 2√29 / 2 = √29

Find centre from mid point formula. {1/2 (x1 + x2) , 1/2 (y1 + y2)}

= {1/2 (1 - 3) , 1/2 (-3 + 7)}

= (-1,2)

Eqn of circle centre (a,b) and of radius r is : (x - a)² + (y - b)² = r²


(x + 1)² + (y - 2)² = (√29)²


(x + 1)² + (y - 2)² = 29

Answer 3

?

Answer 4

(x - 1)² + (y - 4)² = 100 i believe

Answer 5

The equation of the line through point (- 4, 0) and parallel to the y-axis is
x = -4
y = -4
x + y = -4

Answer 6

@SkaterBoyShawn