Mathematics: Find the equation of the circle tangent to the line 4x-3y+12=0 at (-3 0)

Find the equation of the circle tangent to the

Ответ:

Sqeauky

15.03.2022

A circle has the equation $x^{2} + y^{2} = r^{2}.$
What would you like the radius to be? Lets say the radius is 5 since it will work out well with our tangent line. Now there are two places this line could go - it could go left of the line or right of the line - lets say to the right. This would put our center at the point (1,-3). Therefore the equation would be
$(x-1)^{2} + (y +3)^{2} = 25$
If you plug in the point (-3,0) it is on the circle and the line is tangential to the circle.