Methods: If the linear equation is known as Ax+By+C 1=0, (a, b, C 1 are constants).

1. Let the equation of the straight line parallel to the known straight line and tangent to the ellipse be: AX+By+C2=0, where C2 is a constant.

2. Simultaneous elliptic equation, eliminating an unknown number (such as Y) and getting a quadratic equation about X;

3. Make the judgment formula equal to 0 and calculate the value of C2 (there are two);

4. Substitute the quadratic equation about X to find the abscissa of the tangent point, and then substitute it into the linear equation AX+By+C2=0 to find the ordinate.

Note: There are two solutions, one is the point with the smallest distance and the other is the point with the largest distance.

5. For the required distance, you can use the distance formula between two parallel lines: d=|C2-C 1|/√(A? +B？ )