Question types

Straight Lines question types

59 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

59
Questions
6
Question groups
5
Question types
Sample Questions

Straight Lines questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

The distance between the lines y = mx + c1 and y = mx + c2 is:

  1. $\frac{\text{c}_1-\text{c}_2}{\sqrt{\text{m}^2+1}}$

  2. $\frac{|\text{c}_1-\text{c}_2|}{\sqrt{1+\text{m}^2}}$

  3. $\frac{\text{c}_2-\text{c}_1}{\sqrt{1+\text{m}^2}}$

  4. $0$

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The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is:

  1. x - y = 5
  2. x + y = 5
  3. x + y = 1
  4. x - y = 1
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The equations of the lines passing through the point (1, 0) and at a distance $\frac{\sqrt{3}}{2}$ from the origin, are

  1. $\sqrt{3}\text{x}+\text{y}-\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}-\sqrt{3}=0$

  2. $\sqrt{3}\text{x}+\text{y}+\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}+\sqrt{3}=0$

  3. $\text{x}+\sqrt{3}\text{y}-\sqrt{3}=0,\text{x}-\sqrt{3}\text{y}-\sqrt{3}=0$

  4. None of these.

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One vertex of the equilateral triangle with centroid at the origin and one side as x + y - 2 = 0 is:

  1. (-1, -1)
  2. (2, 2)
  3. (-2, -2)
  4. (2, -2)

[Hint: Let ABC be the equilateral triangle with vertex A (h, k) and let $\text{D}(\alpha,\beta)$ be the point on BC. Then $\frac{2\alpha+\text{h}}{3}=0=\frac{2\beta+\text{k}}{3}.$ Also $\alpha+\beta-2=0$ and $\frac{\text{k}-0}{\text{h}-0}\times(-1)=-1\Big].$

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The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are $\text{y}-3=(2\pm\sqrt{3})(\text{x}-2).$
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Equation of the line passing through the point $(\text{a} \cos^3\theta, \text{a} \sin^3 \theta)$ and perpendicular to the line $\text{x}\sec\theta+\text{y cosec}\ \theta=\text{a}$ is $\text{x}\cos\theta-\text{y}\sin\theta=\text{a}\sin2\theta.$
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A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
[Hint: $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ where $\frac{1}{\text{a}}+\frac{1}{\text{b}}=\text{constant}=\frac{1}{\text{k}}(\text{say}).$ This implies that $\frac{\text{k}}{\text{a}}+\frac{\text{k}}{\text{b}}=1$ line passes through the fixed point (k, k).]
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Q 203 Marks Question3 Marks
A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.
[Hint: Let the slope of the line be m. Then the equation of the line passing through the fixed point P (x1, y1) is y - y1 = m (x - x1). Taking the algebraic sum of perpendicular distances equal to zero, we get y - 1 = m (x - 1). Thus (x1, y1) is (1, 1).]
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Q 213 Marks Question3 Marks
Show that the tangent of an angle between the lines $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ and $\frac{\text{x}}{\text{a}}-\frac{\text{y}}{\text{b}}=1$ is $\frac{2\text{ab}}{\text{a}^2-\text{b}^2}.$
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Q 223 Marks Question3 Marks
If p is the length of perpendicular from the origin on the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
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Q 233 Marks Question3 Marks
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.
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Find the equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of x-axis.
[Hint: Use normal form, here $\omega =30^\circ.$]
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Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
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Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
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Match the questions given under Column C1 with their appropriate answers given under the Column C2: The value of the λ, if the lines (2x + 3y + 4) + λ (6x - y + 12) = 0 are:
Column C1 Column C2
(a) Parallel to y-axis is (i) $\lambda=-\frac{3}{4}$
(b) Perpendicular to 7x + y - 4 = 0 is (ii) $\lambda=-\frac{1}{3}$
(c) Passes through (1, 2) is (iii) $\lambda=-\frac{17}{41}$
(d) Parallel to x axis is (iv) $\lambda=3$
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