Math help please

Question

Find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.)
Center C(−5, 9), tangent to the y-axis

Answer 1

Start off with the equation of a circle

 

(x - h)² + (y - k)² = r²

 

where:

centerpoint is (h, k)

r is radius

 

Since the circle is tangent to the y-axis, we only need to find the distance between x=0 and x=-5.  That distance is 5, which is also the radius of the circle.  So your equation will be

 

(x + 5)² + (y - 9)² = 25

Answer 2

If the circle with center C(-5,9) is tangent to the y-axis, that means that the circle will touch at y = 0. Therefore, if you were to draw or imagine the circle, it should have a radius r = 5. 

 

A circle with radius, r, centered at (a,b) has the equation:

 

(x-a)² + (y-b)² = r²

 

(x - (-5))² + (y - 9)² = (5)²

 

(x + 5)² + (y - 9)² = 25  (Ans.)