NCERT MATHS NOTES OF STRAIGHT LINES AND CONIC SECTION OF CLASS 11
EXERCISE 2STRAIGHT LINES
Question 1:
Write the equations for the x and y-axes.
Answer :
The y-coordinate of every point on the x-axis is 0.
Therefore, the equation of the x-axis is y = 0.
The x-coordinate of every point on the y-axis is 0.
Therefore, the equation of the y-axis is x = 0.
Question 2:
Find the equation of the line which passes through the point (–4, 3) with slope .
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (–4, 3), whose slope is , is Question 3:
Find the equation of the line which passes though (0, 0) with slope m.
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (0, 0), whose slope is m,is
(y – 0) = m(x – 0)
i.e., y = mx
Question 4:
Find the equation of the line which passes though and is inclined with the x-axis at an angle of 75°.
Answer :
The slope of the line that inclines with the x-axis at an angle of 75° is m = tan 75° We know that the equation of the line passing through point , whose slope is m, is .
Thus, if a line passes though and inclines with the x-axis at an angle of 75°, then the equation of the line is given as Question 5:
Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope –2.
Answer :
It is known that if a line with slope m makes x-intercept d, then the equation of the line is given as y = m(x – d)
For the line intersecting the x-axis at a distance of 3 units to the left of the origin, d = –3.
The slope of the line is given as m = –2
Thus, the required equation of the given line is y = –2 [x – (–3)] y = –2x – 6
i.e., 2x + y + 6 = 0
Question 6:
Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.
Answer :
Question 1:
Write the equations for the x and y-axes.
Answer :
The y-coordinate of every point on the x-axis is 0.
Therefore, the equation of the x-axis is y = 0.
The x-coordinate of every point on the y-axis is 0.
Therefore, the equation of the y-axis is x = 0.
Question 2:
Find the equation of the line which passes through the point (–4, 3) with slope .
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (–4, 3), whose slope is , is Question 3:
Find the equation of the line which passes though (0, 0) with slope m.
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (0, 0), whose slope is m,is
(y – 0) = m(x – 0)
i.e., y = mx
Question 4:
Find the equation of the line which passes though and is inclined with the x-axis at an angle of 75°.
Answer :
The slope of the line that inclines with the x-axis at an angle of 75° is m = tan 75° We know that the equation of the line passing through point , whose slope is m, is .
Thus, if a line passes though and inclines with the x-axis at an angle of 75°, then the equation of the line is given as Question 5:
Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope –2.
Answer :
It is known that if a line with slope m makes x-intercept d, then the equation of the line is given as y = m(x – d)
For the line intersecting the x-axis at a distance of 3 units to the left of the origin, d = –3.
The slope of the line is given as m = –2
Thus, the required equation of the given line is y = –2 [x – (–3)] y = –2x – 6
i.e., 2x + y + 6 = 0
Question 6:
Find the equation of the line which intersects the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.
Answer :