Find An Equation Of The Circle Tangent To The Circle X\Xb2+Y\Xb2=16 And With Center At (0,9), Student2019s Note: When I Find The Equation I Will Also

Find an Equation of the circle tangent to the circle x²+y²=16 and with center at (0,9)

Student's note: When I find the equation I will also Graph it

 

Answer:

x² + (y - 9)² = 25 or x² + y² - 18y = -56

Step-by-step explanation:

Given:

Center of the unknown circle (Circle A) ⇒ (0, 9)

Equation of Circle B ⇒ x² + y² = 16

Tangent define is any line (but in our case a circle) that touches a curved surface in one exact point called point of tangency and does not touch the same curved surface again.

Write the equation for the unknown circle using the given to know what else to find:

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 9)² = r²

x² + (y - 9) = r² (We are to find r or the radius)

Get the center of Circle B which is C = (0, 0)

Through inspection, we can observe that the centers of Circles A and B are aligned at x = 0 or along the y-axis. So, next is to find the radius of Circle B which is 4. Since theyre aligned, we can just subtract 4 from 9 (If yore confused why I did this, pm me) and we now found the value of Circle As r which is 5. We now have x² + (y - 9)² = 25.

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