Find the standard equation of the circle: C(-5,6) tangeant to y axis?

2 Answers
Jun 18, 2018

See below

Explanation:

Circle general equation is

(xa)2+(yb)2=r2 where (a,b) is center and r is radius

If circle must be tangent to y axis, the distance from center to y axis to the given point is |5|=5

The equation is (x+5)2+(y6)2=25 graph{(x+5)^2+(y-6)^2=25 [-21.38, 18.62, -4.8, 15.2]}

Jun 18, 2018

I assume the notation C(5,6) means the center is at (xc,yc)=(5,6)

Since the circle is given as tangent to the y-axis
the distance from the center to the y-axis (i.e. the radius) is 5
(since all points on the y-axis have x=0, the tangent point will be (0,6))

The required result may depend upon your understanding of what is meant by "the standard equation" for a circle.

I will use
XXX(xxc)2+(yyc)2=r2
as the "standard form" for a circle with center (xc,yc) and radius r.

So, in this case we have
XXX(x+5)2+(y6)2=52

...or, maybe your version of the standard form might be an expansion of this:
XXXx2+10x+y212y+36=0