Tangent to y axis with center(-3,4) whats the eqn of circle?

In summary, the center of the circle is located at (-3, 4) and it is tangent to the y-axis. To find the equation of the circle, the radius must be determined. The radius is found by calculating the distance between the center and the point of tangency on the y-axis. In this case, the radius is 3 units and therefore the equation of the circle is (x+3)^2 + (y-4)^2 = 9.
  • #1
aisha
584
0
the center is (-3,4) and tangent to the y-axis

how will I find the equation of the circle?

I know what tangent means but at what point? Can someone give me a clue? :rolleyes:
 
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  • #2
I am pretty rusty at this, and I am not sure I understand the wording, but could it simply mean that your circle touches the point (0,4) on the y-axis? I am assuming that the line x = 0 is tangent to the curve.
 
  • #3
I think the radius is 3

therefore the equation of the circle is

[tex] (x+3)^2 + (y-4)^2 = 9 [/tex]

is this correct?
 
  • #4
that's fine~
 
  • #5
how come the radius wasnt 4?
 
  • #6
the center is at [itex](-3, 4)[/itex] and the circle is tangent to the [itex]y[/itex] axis, which implies that it is tangent at [itex](0, 4)[/itex]. Thus the radius is the distance between [itex](0, 4)[/itex] and [itex](-3, 4)[/itex] which is clearly 3.
 

1. How do you find the equation of a circle with a center at (-3,4) that is tangent to the y-axis?

The equation of a circle with a center at (-3,4) that is tangent to the y-axis can be found using the formula (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius. Since the circle is tangent to the y-axis, the x-coordinate of the center (-3) will be equal to the radius (r), so the equation can be simplified to (x+3)^2 + (y-4)^2 = 9.

2. Is the circle centered at (-3,4) tangent to the y-axis?

Yes, the circle is tangent to the y-axis because it only touches the y-axis at one point, which means it has a slope of 0 at that point.

3. How can you graph a circle with a center at (-3,4) that is tangent to the y-axis?

To graph a circle with a center at (-3,4) that is tangent to the y-axis, plot the center point (-3,4) and then use the radius value (r) to plot a point on the y-axis at (0,4). From there, you can draw the circle by using a compass to create a circle with a radius of r centered at (-3,4).

4. What is the radius of the circle with a center at (-3,4) that is tangent to the y-axis?

The radius of the circle is equal to the distance between the center (-3,4) and any point on the circle that is tangent to the y-axis. In this case, the radius is equal to the x-coordinate of the center, which is 3.

5. Can you find the equation of a circle using a point on the circumference and the center point?

Yes, the equation of a circle can be found using the formula (x-h)^2 + (y-k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius. The point on the circumference can be used to determine the value of r, and the center point can be used to determine the values of h and k.

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