A point Y moves such that its distance from point B (1,2) is constant. Given that x=k is the tangent of the locus of Y , express the equation of the locus in terms of k.

Answer 1

constant distance from a point is a circle, centered at the point

x = k is a vertical line, tangent to the circle
so the radius of the circle is k-1

(x - 1)² + (y - 2)² = (k - 1)²