Straight Lines · Question 22

JEE Main 2025 (Online) 3rd April Evening ShiftMCQMedium📈 Topic in 10% papers+4−1

Consider the lines x(3 + 1) + y(7 + 2) = 17 + 5, being a parameter, all passing through a point P. One of these lines (say L) is farthest from the origin. If the distance of L from the point (3, 6) is d, then the value of d2 is

Answer

(2) 20

Solution

(x + 2y - 5) + (3x + 7y - 17) = 0

All lines pass through the intersection of x + 2y = 5 and 3x + 7y = 17:

y = 2, x = 1

P(1, 2)

The line through P farthest from the origin is perpendicular to OP.

Slope of OP = 2

slope of L = - 12

L: y - 2 = - 12(x - 1) x + 2y - 5 = 0 (member with = 0)

d = |3 + 12 - 5| 1 + 4 = 10 5 = 2 5

d2 = 20

Answer: (2)

JEE Main 2025 (Online) 3rd April Evening Shift

Keep practising — Straight Lines

Let the area of the triangle formed by a straight line L : x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of 45 with the positive x-axis, then the value of b2 + c2 is :

JEE Main 2025 (Online) 2nd April Evening Shift

Let A(4, -2), B(1, 1) and C(9, -3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and AB of the triangle ABC respectively, is .

JEE Main 2025 (Online) 2nd April Evening Shift

Let be a triangle formed by the lines 7x - 6y + 3 = 0, x + 2y - 31 = 0 and 9x - 2y - 19 = 0. Let the point (h, k) be the image of the centroid of in the line 3x + 6y - 53 = 0. Then h2 + k2 + hk is equal to :

JEE Main 2025 (Online) 29th January Morning Shift

Two equal sides of an isosceles triangle are along -x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum of all possible distinct values of m is:

-2 10
12
-6
6

JEE Main 2025 (Online) 28th January Evening Shift

All Straight Lines PYQs →

PDFDownload Straight Lines PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇

All JEE Main Mathematics chapters

Class 11Sets Relations and Functions Trigonometric Functions Complex Numbers and Quadratic Equations Permutations and Combinations Binomial Theorem Sequences and Series Straight Lines Conic Sections Introduction to Three Dimensional Geometry Limits and Derivatives Statistics Probability

Class 12Relations and Functions (Class 12)Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Application of Derivatives Integrals Application of Integrals Differential Equations Vector Algebra Three Dimensional Geometry Probability (Class 12)