If P(3, 4) is the mid-point of a line segment between the axes, then what is the equation of the line?

The base AB of an equilateral triangle ABC with side 8 cm lies along the y-axis such that the mid-point of AB is at the origin and B lies above the origin. What is the equation of line passing through (8, 0) and parallel to the side AC ?

The centre of the circle passing through the origin and making positive intercepts 4 and 6 on the coordinate axes, lies on the line

The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity ?