Answer:
(x - 3)² + (y - 5)² = 16
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
given (h, k ) = (3, 5 ) we require to find r
r is the distance from the centre to a point on the circle
given x = - 1 is a tangent the r is the distance between the x- coordinates
r = | 3 - (- 1) | = | 3 + 1 | = | 4 | = 4
then equation of circle is
(x - 3)² + (y - 5)² = 4² , that is
(x - 3)² + (y - 5)² = 16