NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Ex 9.2
In Exercises 1 to 8, find the equation of the line which satisfy the given conditions:
Ex 9.2 Class 11 Maths Question 1.
Write the equations for the x- and y-axes.
Solution:
We know that the y-coordinate of each point on the x-axis is 0.
If P(x, y) is any point on the x-axis, then y = 0.
∴ Equation of x-axis is y = 0.
Also, we know that the x-coordinate of each point on the y-axis is 0.
If P(x, y) is any point on the y-axis, then x = 0.
∴ Equation of y-axis is x = 0.
Ex 9.2 Class 11 Maths Question 2.
Passing through the point (-4, 3) with slope ½.
Solution:
We know that the equation of a line with slope m and passing through the point (x0, y0) is given by (y – y0) = m (x – x0).
Ex 9.2 Class 11 Maths Question 3.
Passing through (0, 0) with slope m.
Solution:
We know that the equation of a line with slope m and passing through the point (x0, y0) is given by (y – y0) = m(x – x0)
Here, slope = m, x0 = 0, y0 = 0
Required equation is (y – 0) = m(x – 0)
⇒ y = mx.
Ex 9.2 Class 11 Maths Question 4.
Passing through (2, 2√3) and inclined with the x-axis at an angle of 75°.
Solution:
We know that the equation of a line with slope m and passing through the point (x0, y0) is given by (y – y0) = m(x – x0)
Ex 9.2 Class 11 Maths Question 5.
Intersecting the x-axis at a distance of 3 units to the left of origin with slope -2.
Solution:
We know that the equation of a line with slope m and passing through the point
(x0, y0) is given by (y – y0) = m(x – x0).
Here, m = –2, x0 = –3, y0 = 0
Required equation is y – 0 = -2(x + 3)
⇒ 2x + y + 6 = 0
Ex 9.2 Class 11 Maths Question 6.
Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30° with positive direction of the x-axis.
Solution:
We know that the equation of line with slope m and passing through the point (x0, y0) is given by (y – y0) = m(x – x0).
Ex 9.2 Class 11 Maths Question 7.
Passing through the points (-1, 1) and (2, -4).
Solution:
Let the given points be A(-1, 1) and B(2, -4).
We know that the equation of a line passing through two given points (x1, y1) and (x2, y2) is given by:
Ex 9.2 Class 11 Maths Question 8.
The vertices of ∆PQR are P(2, 1), Q(-2, 3) and R(4, 5). Find equation of the median through the vertex R.
Solution:
The vertices of ∆PQR are P(2, 1), Q(-2, 3) and R(4, 5).
Let S be the mid-point of PQ.
Ex 9.2 Class 11 Maths Question 9.
Find the equation of the line passing through (-3, 5) and perpendicular to the line through the points (2, 5) and (-3, 6).
Solution:
Let M(2, 5) and N(-3, 6) be the end points of the given line segment.
Ex 9.2 Class 11 Maths Question 10.
A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1 : n. Find the equation of the line.
Solution:
Let A(1, 0) and B(2, 3) be the given points and the point D divides the line segment in the ratio 1 : n.
Ex 9.2 Class 11 Maths Question 11.
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
Solution:
Let the required line make intercepts a on the x-axis and y-axis.
Then, its equation is x/a + y/b = 1
⇒ x + y = a … (i)
Since (i) passes through the point (2, 3), we have
2 + 3 = a ⇒ a = 5
So, required equation of the line is:
x/5 + y/5 = 1 ⇒ x + y = 5.
Ex 9.2 Class 11 Maths Question 12.
Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
Solution:
Let the intercepts made by the line on the x-axis and y-axis be a and 9 – a respectively.
Then, its equation is
x/a + y/(9−a) = 1
Since it passes through point (2, 2), we have 2/a + 2/(9−a) = 1
⇒ 2(9 – a) + 2a = a(9 – a)
⇒ 18 – 2a + 2a = 9a – a2
⇒ 18 = 9a – a2
⇒ a2 – 9a + 18 = 0
⇒ a2 – 6a – 3a + 18 = 0
⇒ a(a – 6) – 3 (a – 6) = 0
⇒ (a – 3) (a – 6) = 0
⇒ a = 3, 6
Now, if a = 3 ⇒ b = 9 – 3 = 6 and if a = 6 ⇒ b = 9 – 6 = 3
So, the required equation is:
x/3 + y/6 = 1 or x/6 + y/3 = 1
i.e., 2x + y – 6 = 0 or x + 2y – 6 = 0.
Ex 9.2 Class 11 Maths Question 13.
Find equation of the line through the point (0, 2) making an angle 2Ï€/3 with the positive x-axis. Also, find the equation of the line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Solution:
Here, m = tan 2Ï€/3 = −√3
The equation of the line passing through point (0, 2) is y – 2 = −√3(x – 0)
⇒ √3x + y – 2 = 0
The slope of line parallel to √3x + y – 2 = 0 is −√3.
Since, it passes through (0, -2).
So, the equation of line is y + 2= −√3(x – 0)
⇒ √3x + y + 2 = 0.
Ex 9.2 Class 11 Maths Question 14.
The perpendicular from the origin to a line meets it at the point (-2, 9), find the equation of the line.
Solution:
Ex 9.2 Class 11 Maths Question 15.
The length L (in centimetre) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms C.
Solution:
Assuming L along x-axis and C along y-axis, we have two points (124.942, 20) and (125.134, 110). By two-point form, the point (L, C) satisfies the equation
Ex 9.2 Class 11 Maths Question 16.
The owner of a milk store finds that he can sell 980 litres of milk each week at Rs. 14/litre and 1220 litres of milk each week at Rs. 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs. 17/litre?
Solution:
Assuming L (litres) along x-axis and R(rupees) along y-axis, we have two points (980, 14) and (1220, 16).
By two-point form, the point (L, R) satisfies the equation.
Ex 9.2 Class 11 Maths Question 17.
P(a, b) is the mid-point of a line segment between axes. Show that equation of the line is x/a + y/b = 2.
Solution:
Let the line AB makes intercepts c and d on the x-axis and y-axis, respectively.
Ex 9.2 Class 11 Maths Question 18.
Point R(h, k) divides a line segment between the axes in the ratio 1 : 2. Find equation of the line.
Solution:
Let AB be the given line segment making intercepts a and b on the x-axis and y-axis, respectively.
Then, the equation of the line AB is x/a + y/b = 2.
Now, R(h, k) divides the line segment AB in the ratio 1 : 2.
Ex 9.2 Class 11 Maths Question 19.
By using the concept of equation of a line, prove that the three points (3, 0), (-2, -2) and (8, 2) are collinear.
Solution:
Let the given points be A(3, 0), B(-2, -2) and C(8, 2). Then, the equation of the line passing through A and B is:
Related Links:
NCERT Solutions for Maths Class 9