SOLUTION: 6. A circle of radius 5 has its center on the line 3x – 2y + 6 = 0 and the circle is tangent to the y axis. Find its equation. (There are two solutions.)
Algebra.Com
Question 129347: 6. A circle of radius 5 has its center on the line 3x – 2y + 6 = 0 and the circle is tangent to the y axis. Find its equation. (There are two solutions.)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation
Subtract 3x from both sides
Subtract 6 from both sides
Divide both sides by -2 to isolate y
Break up the fraction
Reduce
Since the circle is tangent to the y-axis and the radius is 5 units, this means that the center must be either at or (since at these x-values, the distance from the y-axis to those points is 5 units)
So let's find the circle at the x value
Start with the given equation
Plug in
Multiply
Combine like terms
So the center of the first circle is )
So this means that the equation of the first circle is
----------------------------------------------------
So let's find the circle at the x value
Start with the given equation
Plug in
Multiply
Combine like terms
So the center of the second circle is )
So this means that the equation of the second circle is
RELATED QUESTIONS
a circle has its center on the line 3x-2y-22=0 and tangent to the y-axis at (0,1). Find... (answered by Alan3354)
A circle has its center at (-4, -2) and is tangent to the line 3x+4y-5=0. What is the... (answered by josgarithmetic)
a circle of radius 5 units has its center in the first quadrant, touches the x-axis and... (answered by josmiceli)
Find the equation of the circle in general form, tangent to 5-y=3 at (2,7) and its center (answered by Cromlix)
Write an equation of a circle that is tangent to the y-axis and has its center at... (answered by macston)
A circle touches the x axis at the point P(-3,0) and its center C lies on the line... (answered by MathLover1,ikleyn,Alan3354)
A unit circle has its center at (5,0) and a second circle with a radius of 2 units has... (answered by ikleyn)
The circle is tangent to y-axis, and the center is at (5, 3). Find the equation of a... (answered by dkppathak)
The straight line 3x-4y-3=0 cuts the circle x^2+y^2-4x-2y+4=0. Find (i)the coordinates of (answered by Alan3354,ikleyn)