Question

Center (10,(5)/(a)) and tangent to the y-axis

Answer 1

To determine the equation of a circle with center (h, k) and radius r, we use the formula (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (10, 5/a) and the circle is tangent to the y-axis, which means the x-coordinate of the center is equal to the radius.

Step-by-step explanation:

To determine the equation of a circle with center (h, k) and radius r, we use the formula (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (10, 5/a) and the circle is tangent to the y-axis, which means the x-coordinate of the center is equal to the radius. Therefore, we have (10-h)^2 + (0-k)^2 = (10)^2. Simplifying this equation will give us the value of h, which represents the x-coordinate of the center.

Step-by-step explanation:

1. 
   
3. Expand the equation using the binomial theorem: (10-h)(10-h) + (-k)(-k) = 100
4. 
   
6. Simplify the equation: 100 - 20h + h^2 + k^2 = 100
7. 
   
9. Combine like terms and rearrange the equation: h^2 - 20h + k^2 = 0
10. 
    
12. Since the circle is tangent to the y-axis, the x-coordinate of the center is equal to the radius: h = 10