In the xy-plane, circle C has center (1,0) and radius 2. If line k is

To find if line K is tangent to the circle C

line k is parallel to the y-axis

Statement 1

Line k passes through the point (−1,0).

Since the line passes though (-1,0) and the line is parallel to y axis, the equation of the line is x = -1

Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1

Hence the line is tangent to the circle

Statement 1 is sufficient

Statement 2

Line k passes through the point (−1,−1).

Since the line passes though (-1,-1) and the line is parallel to y axis, the equation of the line is x = -1 => the line also passes through (-1,0-)

Since the circle has center (1,0) and radius 2, it passes through (-1,0). This is the only point that the circle passes through where x-coordinate is -1

Hence the line is tangent to the circle

Statement 2 is sufficient

Hence option D