Mathematics
Mathematics
Problem
One of the lines of a pair cuts the axes at and . The other line is given by . a. (i) Obtain the equation of the first line in standard form. b. (ii) Solve the two equations simultaneously to find their point of intersection. c. (iii) Determine the area of the triangle formed by the two lines and the -axis.Intuitive explanation
The key is recognizing that "pair of lines" usually means two lines whose product gives a second-degree equation, and that equation often has special structure—like representing a pair of straight lines through a common point or satisfying a geometric condition. First, find the equation of the line through and using the intercept form. Then use the constraint that both lines satisfy (whether they pass through a common point, or their combined equation has a particular property) to determine what the "pair" relationship tells you about the second line.
Intuitive explanation
The key is recognizing that "pair of lines" usually means two lines whose product gives a second-degree equation, and that equation often has special structure—like representing a pair of straight lines through a common point or satisfying a geometric condition. First, find the equation of the line through and using the intercept form. Then use the constraint that both lines satisfy (whether they pass through a common point, or their combined equation has a particular property) to determine what the "pair" relationship tells you about the second line.