Pair of lines

Q.

Equation of line parallel to the line Ax + By + C = 0 is:

1. x + y = - C

2. x + y + k = 0.

3. Bx + Ay = C

4. Ax + By + k = 0

Q.

The equation of a line with x intercept 4 and y intercept 3 is given by

1. x/3-y/4=1

2. x/3+y/4=1

3. x/4+y/3=1

4. x/4-y/3=1

Q.

If 0 $\le$ Argz $\le \frac{\pi }{4}$, then the least value of $\sqrt{2}$ |2z - 4i| is

1. 6

2. 1

3. 2

4. 4

Q.

The equation of the line parallel to the line 2x – 3y = 1 and passing through the middle point of the line segment joining the points (1, 3) and (1, –7), is:

1. 3x – 2y + 8 = 0

2. 2x – 3y – 8 = 0

3. 2x + 3y – 5 = 0

4. 4x – 6y + 7 = 0

Q.

Write converse of the following statement.
If two lines are parallel, then they do not intersect in the same plane'.

Q.

Find the equation of the line parallel to the line 5x – 4y + 3 = 0 and passing through the point (2, 5) is:

1. 5x – 4y + 20 = 0

2. 5x – 4y + 10 = 0

3. 4x – 5y + 20 = 0.

4. 4x – 5y + 10 = 0.

Q.

The slope intercept form of the line 2x+2y=7 and the value of slope and y intercept are

1. 2y=-2x +7; slope = -2, y intercept =7

2. 2x=-2y+7; slope=-2, y intercept=7

3. y= -x+(7/2) ; slope= -1, y intercept =7/2

4. 

Q.

The equation 2x² - 3xy + 5y² + 6x - 3y + 5 = 0 represents.

1. A parabola

2. A hyperbola

3. An ellipse

4. A pair of straight lines

Q.

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

1. 2

2. 8

3. 4

4. 16

Q. Find the equations to the straight lines passing through the point (3, −2) and inclined at 60° to the line $\sqrt{3}x+y=1$.

Q. The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is
(a) 3x + 2y − 63 = 0
(b) 3x + 2y − 2 = 0
(c) 2y − 3x − 2 = 0
(d) none of these

Q. If Z is a complex number such that $\left|z\right|$ greater than or equal to 2, then the minimum value of $|z+\frac{1}{2}|$.

1. 

2. 

3. 

4. Less than

Q. Find the equation of the straight line passing through the point of intersection of 2x + 3y + 1 = 0 and 3x − 5y − 5 = 0 and equally inclined to the axes.

Q. Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y − 5 = 0.

Q. 21) Find the equation of the line perpendicular to the line whose equation is 6x - 7y + 8 = 0 and that passes through the point of intersection of the two lines whose equations are 2x - 3y - 4 = 0 and 3x + 4y - 5 = 0.

Q. The locus of the point of intersection of the lines $\sqrt{3}x-y-4\sqrt{3}\mathrm{\lambda }=0\mathrm{and}\sqrt{3}\mathrm{\lambda }x+\mathrm{\lambda }y-4\sqrt{3}=0$ is a hyperbola of eccentricity
(a) 1
(b) 2
(c) 3
(d) 4

Q. Find the equation of the straight lines passing through the origin and making an angle of 45° with the straight line $\sqrt{3}x+y=11$.

Q. Find the equation of a straight line passing through the point of intersection of x + 2y + 3 = 0 and 3x + 4y + 7 = 0 and perpendicular to the straight line x − y + 9 =0

Q. Show that the straight lines given by (2 + k) x + (1 + k) y = 5 + 7k for different values of k pass through a fixed point. Also, find that point.

Q. Find the equation of the circle which circumscribes the triangle formed by the lines
(i) x + y + 3 = 0, x − y + 1 = 0 and x = 3
(ii) 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
(iii) x + y = 2, 3x − 4y = 6 and x − y = 0.

Q. Find the coordinates of the incentre and centroid of the triangle whose sides have the equations 3x − 4y = 0, 12y + 5x = 0 and y − 15 = 0.

Q. Find the lines through the point (0, 2) making angles $\frac{\mathrm{\pi }}{3}\mathrm{and}\frac{2\mathrm{\pi }}{3}$ with the x-axis. Also, find the lines parallel to them cutting the y-axis at a distance of 2 units below the origin.

Q. Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is $\sqrt{5}$.

Q. Write the number of points of intersection of the curves $2y=1$ and $y=\cos x,0\le x\le 2\pi$.

Q. If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
(a) (2, 2/3)
(b) (2/3, 2)
(c) (−2, 2/3)
(d) none of these

Q. If the lines p₁ x + q₁ y = 1, p₂ x + q₂ y = 1 and p₃ x + q₃ y = 1 be concurrent, show that the points (p₁, q₁), (p₂, q₂) and (p₃, q₃) are collinear.

Q. Find the point of intersection of the following pairs of lines:
(i) 2x − y + 3 = 0 and x + y − 5 = 0
(ii) bx + ay = ab and ax + by = ab.
(iii) $y=m_{1}x+\frac{a}{m_1}andy=m_{2}x+\frac{a}{m_2}.$

Q. Find the equation of a straight line through the point of intersection of the lines 4x − 3y = 0 and 2x − 5y + 3 = 0 and parallel to 4x + 5y + 6 = 0.

Q. 19) The equation of the line passing through the point (c, d) and parallel to the line ax + by +c = 0is :

(A) a(x + c) + b(y + d) = 0 (B) a(x + c) - b(y + d) = 0
(C) a(x - c) + b(y - d) = 0 (D) None of these

Q. Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is $\frac{5}{12}$.