Question

Write the equation of the circle graphed below

Answer 1

Answer:

(x-4)² + (y-3)² =29

Step-by-step explanation:

The equation of a circle is

(x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.

In this circle, the center is at (4, 3)  

(x-4)² + (y-3)² = r²

and we have point (-1 ; 1)

r²=(-1-4)² + (1-3)² = 25+4=29

(x-4)² + (y-3)² =29

Answer 2

Answer:

(x - 4)² + (y - 3)² = 29

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (4, 3 )

The radius r is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (4, 3)

r = $\sqrt{(4+1)^2+(3-1)^2}$

  = $\sqrt{5^2+2^2}$

   = $\sqrt{25+4 }$ = $\sqrt{29}$

Then

(x - 4)² + (y - 3)² = ($\sqrt{29}$ )² , that is

(x - 4)² + (y - 3)² = 29 ← equation of circle