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

[thorpelizts]

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

how do i even begin?

 

[Wilmer]

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".

 

[Sudharaka]

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.

 

[soroban]

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: .(x-h)^2 + (y-k)^2 \:=\:r^2
. . where (h,k) is the center and r is the radius.

                            |
                * * *       |
            *           *   |
          *               * |
         *                 *|
                            |
        *              r    *
        *         * - - - - *4
        *      (-3,4)       *
                            |
         *                 *|
          *               * |
            *           *   |
                * * *       |
                            |
    - - - - - - - + - - - - + - - -
                 -3         |

You know h = -3,\;k=4.

Can you guess what the radius is?

 

[MarkFL]

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

 

[CaptainBlack]

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