Pair of Straight Lines - Maharashtra Board STD 12 Science Maths Questions

Q 1Answer the following questions in short.1 Mark

Find the separate equations of the lines represented by $x^2-y^2+x-y=0$.

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Q 2Answer the following questions in short.1 Mark

Write the separate equations of lines represented by the equation $5 x^2-9 y^2=0$.

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Q 3Solve the Following Question.(2 Marks)2 Marks

Find the value of $K$, if the sum of the slopes of the lines represented by $x^2+K x y-3 y^2=0$ is twice their product.

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Q 4Solve the Following Question.(2 Marks)2 Marks

Find $' k\ '$, if the equation $k x y+10 x+6 y+4=0$ represents a pair of straight lines.

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Q 5Solve the Following Question.(2 Marks)2 Marks

If $2 x+y=0$ is one of the lines represented by $3 x^2+k x y+2 y^2=0$ then the value of $k$ is

A
$\frac{1}{5}$
✓
$\frac{11}{2}$
C
$\frac{5}{2}$
D
$\frac{-11}{2}$

Answer: B.

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Q 6Solve the Following Question.(2 Marks)2 Marks

Find the value of $k$, if $2 x+y=0$ is one of the lines represented by $3 x^2+k x y+2 y^2=0$.

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Q 7Solve the Following Question.(2 Marks)2 Marks

Find the angle between the lines represented by $3 x^2+4 x y-3 y^2=0$.

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Q 8Solve the Following Question.(3 Marks)3 Marks

Prove that the acute angle $\theta$ between the lines represented by the equation $a x^2+2 h x y+b y^2=0$ is given by $\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|$

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Q 9Solve the Following Question.(3 Marks)3 Marks

The slopes of the lines given by $12 x^2+b x y-y^2=0$ differ by 7 . Then the value of $b$ is:

A
2
B
$\pm 2$
C
$\pm 1$
D
1

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Q 10Solve the Following Question.(3 Marks)3 Marks

Find the joint equation of the pair of lines through the origin each of which is making an angle of $30^{\circ}$ with the line
$3 x+2 y-11=0$

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Q 11Solve the Following Question.(3 Marks)3 Marks

Find the values of $p$ and $q$, if the following equation represents a pair of perpendicular lines : $p x^2-8 x y+3 y^2+14 x+2 y+q=0$

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Q 12Solve the Following Question.(3 Marks)3 Marks

If angle between the lines represented by $a x^2+2 h x y+b y^2=0$ is equal to the angle between the lines represented by $2 x^2-5 x y+3 y^2=0$, then show that $100\left(h^2-a b\right)=(a+b)^2$.

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Q 13Solve the Following Question.(4 Marks)4 Marks

If the angle between the lines represented by $a x^2+2 h x y+b y^2=0$ is equal to the angle between the lines $2 x^2-5 x y+3 y^2=0$, then show that $100\left(h^2-a b\right)=(a+b)^2$.

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Q 14Solve the Following Question.(4 Marks)4 Marks

Prove that a homogeneous equation of degree two in $x$ and $y$ i.e. $a x^2+2 h x y+b y^2=0$ represents a pair of lines passing through the origin, if $h^2-a b \geq 0$.

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Q 15Solve the Following Question.(4 Marks)4 Marks

If $\theta$ is the measure of the acute angle between the lines represented by the equation $a x^2+2 h x y+b y^2=0$, then prove that $\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|$ where $a+b \neq 0$ and $b \neq 0$. Find the condition for colncident lines.

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Q 16Solve the Following Question.(4 Marks)4 Marks

Show that the equation $x^2-6 x y+5 y^2+10 x-14 y+9=0$ represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines.

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Q 17Solve the Following Question.(4 Marks)4 Marks

If $\theta$ is the measure of acute angle between the palr of lines represented by $a x^2+2 h x y+b y^2=0$, then prove that $\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|, a+b \neq 0$.
Hence find the acute angle between the liens $x^2-4 x y+y^2=0$.

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Pair of Straight Lines question types

Pair of Straight Lines questions

Generate a Pair of Straight Lines paper free

Pair of Straight Lines Maths - Pair of Straight Lines

Pair of Straight Lines question types

Pair of Straight Lines questions

Generate a Pair of Straight Lines paper free