Write the equation of circle with center (1,0),point (3,5) ?

To find the equation of a circle with center (h,k) and a point on the circle (x1,y1), we can use the formula:

(x - h)^2 + (y - k)^2 = r^2

Where (h,k) is the center of the circle, (x1,y1) is a point on the circle, and r is the radius of the circle.

Given that the center of the circle is (1,0) and a point on the circle is (3,5), we can plug these values into the formula:

(x - 1)^2 + (y - 0)^2 = r^2
(3 - 1)^2 + (5 - 0)^2 = r^2
2^2 + 5^2 = r^2
4 + 25 = r^2
29 = r^2

Therefore, the equation of the circle is:

(x - 1)^2 + y^2 = 29

The distance between the center (1,0) and the point (3,5) is the radius of the circle.

$$r = \sqrt{(3-1)^2 + (5-0)^2} = \sqrt{4 + 25} = \sqrt{29}$$

Therefore, the equation of the circle is:

$$(x-1)^2 + (y-0)^2 = 29$$

Simplifying:

$$x^2 -2x +1 +y^2 = 29$$

$$x^2 -2x +y^2 = 28$$