1. Find the equation of the diameter of the circle x^2 + y^2 - 4x + 6y = 14 which passes through the origin.
2. Find the equation of the diameter of the circle x^2 + y^2 -3x + 2y = 26 which cuts the x-axis at an angle of 45 degrees.
to #1.:
Calculate the coordinates of the centre of the circle by completing the squares:
The line in question has to pass through (2, -3) and the origin.
You should get:
to #2:
Calculate the coordinates of the centre of the circle by completing the squares:
There are two cases possible if the x-axis and a straight line include an angle of 45°: The slope of the line can be m = 1 or m = -1
Use the point-slope-formula to calculate the equation of the line:
a) m = 1:
b) m = -1