Question

What is an equation of a circle whose center is at (2, -4) and is tangent to the line x = -2

Answer 1

Answer:

$(x-2)^{2} +(y+4)^{2} = \frac{4}{5}$

Step-by-step explanation:

Given that the center of the circle is: (2, -4)

tangent to the line x = -2

The equation of a circle has the following formula:

$(x-a)^{2} +(y-b)^{2} = r^{2}$ where a, b is the  center and r is the radius

The distance between the circle and the tangent line is:

d = $\frac{2*1 + 2}{\sqrt{2^{2}+4^{2}} }$ = $2\frac{\sqrt{5} }{5}$

d = r so $d^{2} =r^{2}$ = $(2\frac{\sqrt{5} }{5})^{2}$ = $\frac{4}{5}$

the equation of the circle is:

$(x-2)^{2} +(y+4)^{2} = \frac{4}{5}$