The following question taken from Maths IIT JEE papers is from the topic Lines, and appeared in JEE 1991.

Find the equation of the line passing through the point (2, 3) and making intercept of length 3 units between the lines y = 2x + 2 and y + 2x = 5.

It can be observed from the equations that the lines are parallel to each other. The diagram illustrating the question is drawn for better understanding.
The first thing that needs to be done in this question is to find out the angle that the line makes with the x-axis. The parametric form of equation is used to solve this question ((x – 2/cos θ) = (y – 3/sin θ) = r), where θ is the angle the line makes with the x-axis. Here r would be at the point A on the line y + 2x = 2 as seen in the diagram. Deriving the value of x from the parametric equation, it can be substituted in the equations of the two lines.
The coordinates of A and B are derived from the parametric equation. After this the substitution in the equations of the lines is done. Now solving the equations of the lines, the value of θ can be derived. This is the value required to find the required equation of the line. Now the equation can be derived smoothly.
As seen in the question the basic concepts of Trigonometry also find application here. Thus one must always remember to be thorough with the concepts of all the chapters. Use proper books and remember not to jump from one IIT book or AIEEE book to another while understanding concepts, because the explanation methods in no two preparation books are alike, which might create a lot of confusion.
The essence of Coordinate Geometry is this: The position of different points in space can be described mathematically, and the relationship between these points (the lines joining them) can be expressed in the form of equations. It is not very difficult to master and one can use the basic IIT preparation books like NCERT (CBSE XI and CBSE XII books) to understand the concepts of all such topics.
The NCERT books are always a good place to start. Students of CBSE would not face a problem as these are the prescribed course books for them. The students of other boards can use their own course books for basic conceptual understanding.
Also one must understand the problem solving techniques and practice enough problems so that the techniques come naturally to him/her during the exam. For problem solving and practice, you can choose as many different books for IIT JEE and books for AIEEE as possible because when it comes to practice, the more the better.

 

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