SOLUTION: A circle touches the x axis at the point P(-3,0) and its center C lies on the line 2x+y+1=0. Find: (a)coordinates of C (b)radius of the circle (c)equation of the circle

Algebra ->  Circles -> SOLUTION: A circle touches the x axis at the point P(-3,0) and its center C lies on the line 2x+y+1=0. Find: (a)coordinates of C (b)radius of the circle (c)equation of the circle      Log On


   

Question 1129367: A circle touches the x axis at the point P(-3,0) and its center C lies on the line 2x+y+1=0. Find:
(a)coordinates of C
(b)radius of the circle
(c)equation of the circle
Found 3 solutions by MathLover1, ikleyn, Alan3354:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find:
(a) coordinates of C
center C (h,k) lies on a intersection of the line 2x%2By%2B1=0 is perpendicular to the given line that passes through the point P(-3,0)
find a tangent line
2x%2By%2B1=0.........find slope
y=-2x-1.....eq.1-> m=-2
the line perpendicular to a given line will have a slope -1%2Fm=-1%2F-2=1%2F2
equation is:
y-0=%281%2F2%29%28x-%28-3%29%29
y=%281%2F2%29%28x%2B3%29
y=%281%2F2%29x%2B3%2F2.....eq.2
find intersection of these two lines:
%281%2F2%29x%2B3%2F2=-2x-1
%281%2F2%29x%2B2x=-3%2F2-1
%285%2F2%29x=-5%2F2
x=-1
y=-2%28-1%29-1.....eq.1-> y=1
intersection point: (-1,1)
so,C (h,k) = C(-1,1)
(b)radius of the circle
distance from C (-1,1) to P(-3,0)
r=sqrt%28%28-1-%28-3%29%29%5E2%2B%281-0%29%5E2%29
r=sqrt%284%2B1%29
r%5E2=5
(c)equation of the circle
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
%28x%2B1%29%5E2%2B%28y-1%29%5E2=5




Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.
Since the circle touches the x-axis at the point P(-3,0), its center has x-coordinate equal to -3.


Since the center has x-coordinate equal to -3 and lies on the line 2x + y + 1 - 0,
its y-coordinate is y = -2x-1 = -2*(-3)-1 = 6-1 =5.


So, the coordinates of the center of the circle are (-3,5).


Then the radius of the circle is equal to 5 units.


Then the equation of the circle is  %28x-%28-3%29%29%5E2 + %28y-5%29%5E2 = 5%5E2,  or,  equivalently


    %28x%2B3%29%5E2 + %28y-5%29%5E2 = 25.

Solved.

Ignore each and every different answer.


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A circle touches the x axis at the point P(-3,0) and its center C lies on the line 2x+y+1=0. Find:
(a)coordinates of C
(b)radius of the circle
(c)equation of the circle
============
"touches" means tangent.
--> the radius is on the line perpendicular to the x-axis thru the point (-3,0)
----
The intersection of the 2 lines is the center.
etc.