In order to prove that QR passes through point O, we can use the fact that PQ and PR are both inclined equally on the line xy=c2. This means that the angle formed by PQ and PR at point O must be equal, making O the midpoint of QR. Therefore, QR must pass through point O.
In this context, "inclined equally" means that PQ and PR form equal angles with the line xy=c2. This means that the slope of PQ and PR are equal, making them parallel lines.
We can prove that PQ and PR are inclined equally by calculating their slopes using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are any two points on the lines. If the slopes are equal, then we can conclude that PQ and PR are inclined equally.
Yes, we can represent this proof using a diagram of a coordinate plane, with points P, Q, R, and O marked. We can also draw the line xy=c2 and indicate the slopes of PQ and PR to visually demonstrate the concept of "inclined equally".
Yes, there are other ways to prove that QR passes through point O. For example, we can use the slope-intercept form of a line (y=mx+b) to show that the y-intercept of both PQ and PR is equal to c2/2. This means that point O, with coordinates (0,c2/2), lies on both lines, proving that QR passes through O.