Answer:
The student's question involves converting polar coordinates to Cartesian coordinates and finding distances between points in a Cartesian coordinate system using respective formulas.
Step-by-step explanation:
The question involves calculating Cartesian coordinates from given polar coordinates and determining distances between points in a Cartesian plane. To convert polar coordinates to Cartesian coordinates (x, y), we use the equations x = r · cos(θ) and y = r · sin(θ), where r is the radius (distance from the origin) and θ is the angle in radians from the positive x-axis. To find the distance between two points, A(x1, y1) and B(x2, y2), in the Cartesian plane, we use the distance formula: d = √[(x2 - x1)2 + (y2 - y1)2].
For example, point M given as M(-4, 6) is not on the circle but may be part of a different question. The letter d refers to various concepts in the questions provided, such as the distance between points in the Cartesian coordinate system or the spacing between the planes in optics and reflection questions.