A

Step 1: Evaluate the Assertion: The assertion states that "Parallactic angle measures the angle between two directions along which the planet is viewed." This is true, as the parallactic angle is indeed the angle between lines of sight from two different points of observation to a celestial object, such as a planet.

Step 2: Evaluate the Reason: The reason claims, "Parallax method utilizes the angle subtended by a planet at two locations of observations." This is also true, because the parallax method involves measuring the apparent shift in position of the planet due to the change in observer's location, which is defined by the angle subtended at the planet.

Step 3: Establish the relationship: The reason provided directly supports the assertion, as it explains how the parallactic angle is utilized in measuring angles from different observational points. Thus, the reason is indeed a correct explanation of the assertion.

Therefore, both the assertion and reason are true, and the reason is the correct explanation of the assertion. Hence, the correct option is A.