Equation of Circle Centered at (-3,4) Touches Y-Axis

In summary: SEIn summary, to find the equation of a circle whose centre is (-3,4) and touches the y-axis, you can use the formula (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the centre and r is the radius. By setting x=0 and solving for r, you can find the radius of the circle.
  • #1
thorpelizts
6
0
Find the equation of the circle whose centre is (-3,4) and which touches the y-axis.

how do i even begin?
 
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  • #2
thorpelizts said:
Find the equation of the circle whose centre is (-3,4) and which touches the y-axis.
how do i even begin?
Teacher gave no instructions, no teaching?
Google "equation of circle".
 
  • #3
thorpelizts said:
Find the equation of the circle whose centre is (-3,4) and which touches the y-axis.

how do i even begin?

Hi thorpelizts, :)

Let \(P\equiv (-3,4)\) and let \(Q\) be the point of intersection of the circle and the y-axis. Since the y-axis is a tangent to the circle, \(PQ\) is perpendicular to the y-axis. Now I am sure you can find the length of \(PQ\) which is the radius of the circle. Can you give it a try?

Kind Regards,
Sudharaka.
 
  • #4
Hello, thorpelizts!

Find the equation of the circle whose centre is (-3,4) and which touches the y-axis.

How do i even begin? . Make a sketch!

You are expected to know this formula: .[tex](x-h)^2 + (y-k)^2 \:=\:r^2[/tex]
. . where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

Code: 
                            |
                * * *       |
            *           *   |
          *               * |
         *                 *|
                            |
        *              r    *
        *         * - - - - *4
        *      (-3,4)       *
                            |
         *                 *|
          *               * |
            *           *   |
                * * *       |
                            |
    - - - - - - - + - - - - + - - -
                 -3         |
You know [tex]h = -3,\;k=4.[/tex]

Can you guess what the radius is?
 
  • #5
While soroban's method is easiest, you might also consider we want the solution of the systerm:

(x + 3)2 + (y - 4)2 = r2

x = 0

to have one real root.

Substitute into the first equation from the second:

(0 + 3)2 + (y - 4)2 = r2

(y - 4)2 + 9 - r2 = 0

We want this quadratic to have one root, hence the discriminant must be zero:

02 - 4(1)(9 - r2) = 0

r = 3
 
  • #6
thorpelizts said:
Find the equation of the circle whose centre is (-3,4) and which touches the y-axis.

how do i even begin?

You begin by drawing a picture.

CB
 

FAQ: Equation of Circle Centered at (-3,4) Touches Y-Axis

What is the equation of a circle centered at (-3,4) that touches the y-axis?

The equation of a circle centered at (-3,4) that touches the y-axis can be written as (x+3)^2 + (y-4)^2 = r^2, where r is the radius of the circle.

How do you find the radius of a circle centered at (-3,4) that touches the y-axis?

The radius of the circle can be found by calculating the distance between the center (-3,4) and any point on the circle that touches the y-axis. This distance will be equal to the radius of the circle.

Can a circle centered at (-3,4) touch the y-axis at more than one point?

No, a circle can only touch the y-axis at one point if it is centered at (-3,4). This is because the distance from the center to any point on the circle must be equal to the radius of the circle, and there is only one point on the y-axis that is at a specific distance from the center.

How does the value of r affect the size of the circle centered at (-3,4) that touches the y-axis?

The value of r, or the radius, directly affects the size of the circle centered at (-3,4) that touches the y-axis. A larger value of r will result in a larger circle, while a smaller value of r will result in a smaller circle.

Can the equation of a circle centered at (-3,4) that touches the y-axis be written in a different form?

Yes, the equation of a circle centered at (-3,4) that touches the y-axis can also be written as (x+3)^2 + (y-k)^2 = k^2, where k is the distance between the center and the y-axis. This form may be more convenient when finding the radius or graphing the circle.

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