The lines represented by the equation ax 2 (b – c) – xy(ab – bc) + cy 2 (a – b) = 0, are

a(b – c) x – c (a – b)y = 0, x – y = 0

a(b – c)x – c(a – b)y = 0, x + y = 0

If in general quadratic equation f(x, y) = 0, ∆ = 0 and h 2 = ab, then the equation represents

Two perpendicular straight lines

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 10

The distance between the pair of parallel lines x² + 2xy + y² – 8ax – 8ay – 9a² = 0 is

0%
0%
2)
0%
10a
0%

Two lines are given by (x – 2y)² + k(x – 2y) = 0. The value of k so that the distance between them is 3, is

0%
0%
2)
0%
0%
None of these

The pair of straight lines joining the origin to the points of intersection of the line y = 2√2 x + c and the circle x² + y² = 2 are at right angles, if

0%
c2 – 4 = 0
0%
c2 – 8 = 0
0%
c2 – 9 = 0
0%
c2 – 10 = 0

The equation of pair of lines joining origin to the points of intersection of x² + y² = 9 and x + y = 3 is

0%
(x + y)2 = 9
0%
x2 + (3 – x)2 = 9
0%
xy = 0
0%
(3 – x)2 + y2 = 9

The equation of the bisectors of the angle between lines represented by equation 4x² – 16xy – 7y² = 0 is

0%
0%
2)
0%
0%

If y = mx be one of the bisectors of the angle betweem the lines ax² - 2hxy + by² = 0 ,is

0%
h(1 + m+ m (a – b) = 0
0%
h(1 – m+ m (a + b) = 0
0%
h(1 – m+ m (a – b) = 0
0%
h(1 + m+ m (a + b) = 0

If the bisectors of the angles between the pairs of lines given by the equation ax² + 2hxy + by² = 0 and ax² + 2hxy + by² + λ(x² + y²) = 0 be coincident, then λ =

0%
a
0%
b
0%
h
0%
Any real number

If r(1 – m²) + m(p – q) = 0, then a bisector of the angle between the lines represented by the equation px² – 2rxy + qy² = 0, is

0%
y = x
0%
y = –x
0%
y = mx
0%
my = x

If the equation ax² + 2hxy + by² = 0 has the one line as the bisector of angle between the co-ordinates axes, then

0%
(a – b)2 = h2
0%
(a + b)2 = h2
0%
(a – b)2 = 4h2
0%
(a + b)2 = 4h2

If the bisectors of the angles of the lines represented by 3x² – 4xy + 5y² = 0 and 5x² + 4xy + 3y² = 0 are same, then the angle made by the lines represented by first with the second, is

0%
30o
0%
60o
0%
45o
0%
90o

Separate equations of lines, for a pair of lines, whose equation is x² + xy – 12y² = 0 are

0%
x + 4y = 0 and x + 3y = 0
0%
2x – 3y = 0 and x – 4y = 0
0%
x – 6y = 0 and x – 3y = 0
0%
x + 4y = 0 and x – 3y = 0

The equation of the lines represented by the equation ab (x² – y²) + (a² – b²) xy = 0 are

0%
ax – by = 0, bx + ay = 0
0%
ax – by = 0, bx – ay = 0
0%
ax + by = 0, bx + ay = 0
0%
ax + by = 0, bx – ay = 0

The straight line 3x + 4y – 5 = 0 and 4x = 3y + 15 intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1,are

0%
0%
2)
0%
0%

The lines represented by the equation ax² (b – c) – xy(ab – bc) + cy² (a – b) = 0, are

0%
a(b – c)x – c(a – b)y = 0, x + y = 0
0%
x + y = 0, x – y = 0
0%
a(b – c) x – c (a – b)y = 0, x – y = 0
0%
None of these

The nature of straight lines represented by the equation 4x² + 12xy + 9y² = 0, is

0%
Real and coincident
0%
Real and different
0%
Imaginary and different
0%
None of the above

The equation of the perpendiculars drawn from the origin to the lines represented by the equation 2x² – 10xy + 12y² + 5x – 16y – 3 = 0 is

0%
6x2 + 5xy + y2 = 0
0%
6y2 + 5xy + x2 = 0
0%
6x2 – 5xy + y2 = 0
0%
None of these

Which of the following second degree equation represents a pair of straight lines ?

0%
x2 – xy – y2 = 1
0%
–x2 + xy – y2 = 1
0%
4x2 – 4xy + y2 = 4
0%
x2 + y2 = 4

A general equation of second degree ax² + by² + 2hxy + 2gx + 2fy + c = 0 represents a pair of straight lines if

0%
h2 = ab
0%
h2 > ab
0%
h2 < ab
0%

If one of the lines represented by the equation ax² + 2hxy + by² = 0 be y = mx, then

0%
bm2 + 2hm + a = 0
0%
bm2 + 2hm – a = 0
0%
am2 + 2hm + b = 0
0%
bm2 – 2hm + a = 0

Maths-Straight Line and Pair of Straight Lines-52159.png

0%
9 : 8
0%
8 : 9
0%
1 : 2
0%
2 : 1

The equation 2x² + 4xy – py² + 4x + qy + 1 = 0 will represent two mutually perpendicular straight lines, if

0%
p = 1 and q = 2 or 6
0%
p = 2 and q = 0 or 6
0%
p = 2 and q = 0 or 8
0%
p = –2 and q = – 2 or 8

If the equation Ax² + 2Bxy + Cy² + Dx + Ey + F = 0 represents a pair of straight lines, then B² – AC

0%
< 0
0%
= 0
0%
> 0
0%
None of these

Maths-Straight Line and Pair of Straight Lines-52163.png

0%
0%
2)
0%
0%

If the slope of one of the lines represented by the equation ax² + 2hxy + by² = 0 be λ times that of the other, then

0%
4λh = ab(1 + λ)
0%
λh = ab(1 + λ)2
0%
4λh2 = ab(1 + λ)2
0%
None of these

Maths-Straight Line and Pair of Straight Lines-52170.png

0%
0%
2)
0%
0%
None of these

Maths-Straight Line and Pair of Straight Lines-52175.png

0%
0%
2)
0%
0%

The equations of the lines represented by the equation ax² + (a + b)xy + by² + x + y = 0 are

0%
ax + by + 1 = 0, x + y = 0
0%
ax + by – 1 = 0, x + y = 0
0%
ax + by + 1 = 0, x – y = 0
0%
None of these

If two sides of a triangle are represented by x² – 7xy + 6y² = 0 and the centroid is (1,0), then the equation of third side is

0%
2x + 7y + 3 = 0
0%
2x – 7y + 3 = 0
0%
2x + 7y – 3 = 0
0%
2x – 7y – 3 = 0

The equation of one of the lines represented by the equation x² + 2xy cot θ – y² = 0, is

0%
x – y cot θ = 0
0%
x + y tan θ = 0
0%
x sin θ + y (cos θ += 0
0%
x cos θ + y (sin θ += 0

The equation of one of the lines represented by the equation pq(x² – y²) + (p² – q²)xy = 0, is

0%
px + qy = 0
0%
px – qy = 0
0%
p2x + q2y = 0
0%
q2x – p2y = 0

The pair of straight lines passing through the point (1,and perpendicular to the pair of straight lines 3x² – 8xy + 5y² = 0, is

0%
(5x + 3y +(x + y += 0
0%
(5x + 3y –(x + y –= 0
0%
(3x + 5y –(x + y += 0
0%
(3x – 5y +(x + y –= 0

If in general quadratic equation f(x, y) = 0, ∆ = 0 and h² = ab, then the equation represents

0%
Two parallel straight lines
0%
Two perpendicular straight lines
0%
Two coincident lines
0%
None of these

The condition of representing the coincident lines by the general quadratic equation f(x,y) = 0, is

0%
∆ = 0 and h2 = ab
0%
∆ = 0 and a + b = 0
0%
∆ = 0 and h2 = ab, g2 = ac, f2 = bc
0%
h2 = ab, g2 = ac and f2 = bc

The joint equation of the straight lines x + y = 1 and x – y = 4, is

0%
x2 – y2 = –4
0%
x2 – y2 = 4
0%
(x + y – 1)(x – y –= 0
0%
(x + y + 1)(x – y += 0

The equation to the pair of straight lines through the origin which are perpendicular to the lines 2x² – 5xy + y² = 0, is

0%
2x2 + 5xy + y2 = 0
0%
x2 +2y2 + 5xy = 0
0%
x2 – 5xy + 2y2 = 0
0%
2x2 + y2 – 5xy = 0

The area of the triangle formed by the lines x² – 4y² = 0 and x = a, is

0%
2a2
0%
2)
0%
0%

The value of λ, for which the equation x² – y² – x – λy – 2 = 0 represents a pair of straight lines, are

0%
3, –3
0%
–3, 1
0%
3, 1
0%
–1, 1

If the lines represented by the equation ax² – bxy – y² = 0 make angles α and β with the x-axis, then tan (α + β )

0%
0%
2)
0%
0%
None of these

Maths-Straight Line and Pair of Straight Lines-52193.png

0%
0%
2)
0%
0%

The angle between the lines represented by the equation 4x² – 24xy + 11y² = 0 are

0%
0%
2)
0%
0%

If the lines represented by the equation 2x² – 3xy + y² = 0 make angles α and β with x-axis, then cot² α + cot² β

0%
0
0%
2)
0%
0%

Angle between the lines joining the origin to the points of intersection of the curves 2x² + 3y² + 10x = 0 and 3x² + 5y² + 16x = 0 is

0%
0%
2)
0%
90o
0%
None of these

The lines (lx + my)² – 3(mx – ly)² = 0 and lx + my + n = 0 form

0%
An isosceles triangle
0%
A right-angled triangle
0%
An equilateral triangle
0%
None of these

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is

0%
30o
0%
45o
0%
60o
0%

The angle between the lines represented by the equation (x² + y²) sin θ + 2xy = 0 is

0%
θ
0%
2)
0%
0%

The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve 3x² + 4xy – 4x + 1 = 0 include an angle

0%
0%
2)
0%
0%

Maths-Straight Line and Pair of Straight Lines-52223.png

0%
3
0%
4
0%
5
0%
6

If two of the three lines represented by the equation ax³ + bx²y + cxy² + dy³ = 0 are perpendicular, then

0%
a2 + d2 = 2ac
0%
a2 + d2 = 2bd
0%
a2 + ac + bd + d2 = 0
0%
a2 + d2 = 4bc

The acute angle formed between the lines joining the origin to the points of intersection of the curves x² + y² – 2x –1 = 0 and x + y = 1, is

0%
0%
tan–12
0%
0%
60o

If the angle 2θ is acute, then the acute angle between x² (cos θ – sin θ) + 2xy cos θ + y² (cos θ + sin θ) = 0 is

0%
2θ
0%
2)
0%
θ
0%

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 10 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Straight Line And Pair Of Straight Lines Quiz 10 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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