Question

fine the equation for the circle with center (-4, 1) and passing through (-1, 4)write the equation

Answer 1

The standard equation of a circle is given by;

(x-a)² + (y-b)² = r²

where (a,b) is the center of the circle and r is the radius of the circle

We already have the center of the circle which is given by (-4,1)

we will have to find the radius of the circle

The radius of the circle is the distance from the center of the circle to point (-1,4)

We can determine the radius by using the distance formula;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

x₁= -4 y₁ = 1 x₂ = -1 y₂=4

Inserting the values into the formula;

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

$d=\sqrt{3^2+3^2}$$d=\sqrt{9+9}=\sqrt{18}$

So r= √18

We will now plug a=-4 b=1 and r= √18 into the circle formula;

(x-a)² + (y-b)² = r²

(x+4)² + (y-1)² = (√18 )²

(x+4)² + (y-1)² = 18