JEE Exam > JEE Notes > Mathematics (Maths) for JEE Main & Advanced > JEE Advanced Previous Year Questions (2018 - 2023): Straight Lines
JEE Advanced Previous Year Questions (2018 - 2023): Straight Lines | Mathematics (Maths) for JEE Main & Advanced PDF Download
2021
Q1: Consider the lines L1 and L2 defined by
For a fixed constant λ, let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P from L2 is λ2. The line y = 2x + 1 meets C at two points R and S, where the distance between R and S is √270. Let the perpendicular bisector of RS meet C at two distinct points R' and S'. Let D be the square of the distance between R' and S'. ]
The value of λ2 is __________. [JEE Advanced 2021 Paper 1]
Ans: 9
According to the question,
Let R ≡ (x1, y1) and S(x2, y2)
∵ C cuts y − 1 = 2x at R and S.
So, 
∵ RS2 = 270 (given)
Q2: Consider the lines L1 and L2 defined by
For a fixed constant λ, let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P from L2 is λ2. The line y = 2x + 1 meets C at two points R and S, where the distance between R and S is √270. Let the perpendicular bisector of RS meet C at two distinct points R' and S'. Let D be the square of the distance between R' and S'. ]
The value of D2 is __________. [JEE Advanced 2021 Paper 1]
Ans: 77.14
According to the question,
Let R ≡ (x1, y1) and S(x2, y2)
∵ C cuts y − 1 = 2x at R and S.
So,
∵ RS2 = 270 (given)
Now, mid-point of RS is 
and slope of RS = 2 and slope of 
On solving x + 2y − 2 = 0 with C, we get
Hence, 
= 
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FAQs on JEE Advanced Previous Year Questions (2018 - 2023): Straight Lines - Mathematics (Maths) for JEE Main & Advanced
| 1. What are some important concepts to understand in straight lines for JEE Advanced? |  |
Ans. Some important concepts to understand in straight lines for JEE Advanced include slope-intercept form, point-slope form, two-point form, intercept form, distance between a point and a line, and equations of parallel and perpendicular lines.
| 2. How can I find the equation of a line knowing its slope and a point it passes through? | |
Ans. To find the equation of a line knowing its slope (m) and a point (x₁, y₁) it passes through, you can use the point-slope form. The equation is given by y - y₁ = m(x - x₁).
| 3. What is the condition for two lines to be parallel? | |
Ans. Two lines are parallel if and only if their slopes are equal. In other words, if the slopes (m₁ and m₂) of two lines are equal, they are parallel.
| 4. How can I find the distance between a point and a line? | |
Ans. To find the distance between a point (x₁, y₁) and a line Ax + By + C = 0, you can use the formula:
Distance = |Ax₁ + By₁ + C| / √(A² + B²)
This formula is derived from the perpendicular distance formula.
| 5. Can you explain the intercept form of a straight line equation? | |
Ans. The intercept form of a straight line equation is given by x/a + y/b = 1, where a and b are the x-intercept and y-intercept of the line, respectively. This form is convenient for determining the intercepts and sketching the line on a coordinate plane.
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