Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter.​

Complete question is;

Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter.​ Write the equation of the circle.

x² + y² - 6x + 2y + 5 = 0

Step-by-step explanation:

The end points of the diameter are;

(4. -3) and (2, 1).

Thus, the centre coordinates will be the midpoint of the diameter endpoints.

Thus;

Centre coordinates = ((4 + 2)/2), ((-3 + 1)/2) = (3, -1)

Diameter;

d = √(1 - (-3))² + (2 - 4)²)

d = √20

d = 2√5

Radius = ½ × diameter

Thus;

r = ½ × 2√5

r = √5

Equation of a circle is;

(x - a)² + (y - b)² = r²

Where;

(a, b) are coordinates of the centre of the circle

r is radius.

Thus;

(x - 3)² + (y - (-1))² = (√5)²

x² - 6x + 9 + y² + 2y + 1 = 5

x² + y² - 6x + 2y + 10 = 5

x² + y² - 6x + 2y + 10 - 5 = 0

x² + y² - 6x + 2y + 5 = 0

left 3, up 4

step-by-step explanation:

just count the values of x & y of the vertex of the graph and see how many units in the x and y direction will get you from the f(x) graph to the f(x) graph

your answer would be 10x - 1