Advertisements
Advertisements
प्रश्न
If P(r, c) is midpoint of a line segment between the axes then show that `x/"r" + y/"c"` = 2
उत्तर
Let AB be the line segment intercepted between the axes.
Let A be (a, 0) and B be (0, b)
Given P(r, c) is the midpoint of AB
∴ (r, c) = `((0 + "a")/2, ("b" +0)/2)`
r = `"a"/2`, c = `"b"/2`
a = 2r, b = 2c
The equation of the line AB having x-intercept a and y-intercept b is `x/"a" + y/"b"` = 1
Substituting for a, b in the above equation, we have
`x/(2"r") + y/(2"c")` = 1
`x/"r" + y/"c"` = 2
APPEARS IN
संबंधित प्रश्न
Find the slope of the following line which passes through the points:
C(−2, 3), D(5, 7)
Find the slope of the following line which passes through the points:
G(7, 1), H(−3, 1)
If the X and Y-intercepts of lines L are 2 and 3 respectively then find the slope of line L.
A line passes through points A(x1, y1) and B(h, k). If the slope of the line is m then show that k − y1 = m(h − x1)
If points A(h, 0), B(0, k) and C(a, b) lie on a line then show that `"a"/"h" + "b"/"k"` = 1
Select the correct option from the given alternatives:
If A is (5, −3) and B is a point on the x-axis such that the slope of line AB is −2 then B ≡
Select the correct option from the given alternatives:
The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is
Answer the following question:
Find the value of k the point P(1, k) lies on the line passing through the points A(2, 2) and B(3, 3)
Find the equation of the lines passing through the point (1,1) with slope 3
Find the equation of the lines passing through the point (1,1) and (– 2, 3)
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400 m from the target, and at the 18th second 800 m away. Find the distance covered by it in 15 seconds
Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using concept of slope
A 150 m long train is moving with constant velocity of 12.5 m/s. Find the equation of the motion of the train
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
If the spring has to stretch to 9 cm long, how much weight should be added?
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table
| Weight (kg) | 2 | 4 | 5 | 8 |
| Length (cm) | 3 | 4 | 4.5 | 6 |
How long will the spring be when 6 kilograms of weight on it?
In a shopping mall there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find the slopes of the escalator at the turning points
Choose the correct alternative:
The y-intercept of the straight line passing through (1, 3) and perpendicular to 2x − 3y + 1 = 0 is
The locus of the midpoint of the portion intercept between the axes by the line xcosa + ysina = P where P is a constant is ______.
The equation of the line passing through the point (–3, 1) and bisecting the angle between co-ordinate axes is ______.
