What is the shortest distance between origin and a line?

Question of The Day21-03-2021

What is the shortest distance between origin and the line 12x + 5y = 26?

Answer

Correct Answer : b ) 2

Explanation :

The shortest distance from a point P (x₁, y₁) to the straight-line having equation Ax + By + c = 0 will be the length of the perpendicular drawn from point P to the line Ax + By + C = 0

Distance=\({|Ax_1+By_1+C| \over \sqrt{A^2+B^2}}\)

Thus, shortest distance between origin (0, 0) and line 12x + 5y – 26 = 0 will be

Distance=\({|0+0-26| \over \sqrt{12^2+5^2}} ={26 \over 13}\)=2 unit

Hence, (b) is the correct answer.

Such type of questions from Coordinate Geometry is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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Shell

Noun: A hard rigid usually large covering of an animal.; The outside part of a fruit or seed.; Something like an external structure that resembles a shell.; A casing without substance.; The hard exterior of an egg.; A hard enclosing cover.