Test: Distance Between Lines - JEE MCQ

# Test: Distance Between Lines - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Distance Between Lines

Test: Distance Between Lines for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Distance Between Lines questions and answers have been prepared according to the JEE exam syllabus.The Test: Distance Between Lines MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Distance Between Lines below.
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Test: Distance Between Lines - Question 1

### If the length of the perpendicular from the origin to the line 3x+2y = 6 is m. What is the value of m?

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Test: Distance Between Lines - Question 2

### What is the angle made by the perpendicular from the origin to the line x+ √3y = 2 with the positive direction of x axis?

Detailed Solution for Test: Distance Between Lines - Question 2

The given equation is
x − √3y = 2
On dividing both sides by
[(−1)2 + (√3)2]1/2 = √4 = 2
= x/2 + √3y/2 = 2/2
= (1/2)x + (√3/2)y = 1
= x cos 60° + y sin 60° = 1
Normal form of any line is : x cosw + y sinw = p
w = 60°

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Test: Distance Between Lines - Question 3

### The slope of a line is 3 and its y intercept is 2.What is the distance of such a line from the point (1,-2)?

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Test: Distance Between Lines - Question 4

What will be the co-ordinates of foot of perpendicular line drawn from the point (-1,3) to the line 3x-4y-16=0?

Detailed Solution for Test: Distance Between Lines - Question 4

The foot of perpendicular can be found by equating the distance between the two points and the distance between point and line. This is found to be (68/25,-49/25).

Test: Distance Between Lines - Question 5

What is the distance of the point (3,3) from the line 2(x-3) = 3(y+5)?

Detailed Solution for Test: Distance Between Lines - Question 5

2(x-3) = 3(y+5)
2x - 6 = 3y + 15
2x - 3y = 21
2x - 3y - 21 = 0
Using distance formula = |ax1 + by1 + c|/(a2 + b2)1/2
= (6-9-21)/((2)2 + (3)2)1/2
= 24/(13)1/2

Test: Distance Between Lines - Question 6

What is the distance between the parallel lines 3(x+y) + 2 = 0 And 6x+6y+28 = 0?

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Test: Distance Between Lines - Question 7

The point on y-axis equidistant from the points (3,2) and (-1,3) is

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Test: Distance Between Lines - Question 8

A point P is in the interior of angle BAC, such that P lies on the bisector of angle BAC. What can be said about the distance of PM if PN = 2cm where PM and PN are perpendiculars from P on the lines BA and AC?

Detailed Solution for Test: Distance Between Lines - Question 8

In Δ PAM & Δ PAN, angle (PAM) = angle (PAN) (Since AP bisects the angle (BAC)) angle (AMP) = angle (ANP) = 900
PA = PA (common)
By AAS congruence, Δ PAM and Δ PAN are congruent.
MP = NP = 2 cm

Test: Distance Between Lines - Question 9

For a line whose equation is √3x + y = 8, the length of the perpendicular from the origin is

Detailed Solution for Test: Distance Between Lines - Question 9

√3x + y - 8
√3x + y = 8
Dividing by √[(√3)2 + (1)2]
= √[3+1]
= √4
= 2
√3x/2 + y/2 = 8/2
√3x/2 + y/2 = 4
x(√3/2) + y(1/2) = 4.....(1)
Normal form of any line : xcos w + ysin w = p....(2)
Comparing (1) and (2)
p = 4

Test: Distance Between Lines - Question 10

The distance between the parallel lines 4x-3y+5 = 0 and 4x-3y+15 = 0 is :

Detailed Solution for Test: Distance Between Lines - Question 10

4x - 3y + 5 = 0,  4x - 3y + 15 = 0
A = 4,  B = -3   c1 = 5,   c2 = 15
|c1 - c2|/[A2 + B2]1/2
= |5 - 15|/[(4)2 + (-3)2]½
= 10/5
= 2

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests