find the equation of a line passing through the point (2,2)and cutting off intercept on the axes whose sum is 9
Answers
Answer:
a-3=0 and a-6=0
Step-by-step explanation:
so..a=3 and a =6 straight line forms
Given:
The point (2,2) and cutting off intercepts on the axes whose sum is 9.
To find:
Find the equation of a line..?
Solution:
The equation of a line in the intercept form is x/a + y/b = 1 -------------•(i).
Here,
a and b are the intercepts on x and y axis respectively.
It is given that
=> a + b = 9
=> b = 9 - a -------------•(ii).
From equation (i) and (ii), we obtain.
=> x/a + y/9 - a = 1 ------------•(iii).
It is given that the line passes through points (2, 2)
Therefore, equation
=> 2/a + 2/9 - a = 1
=> 2[1/a + 1/9 - a] = 1
=> 2[9 - a + a / a(9 - a)] = 1
=> 18/9a - a² = 1
=> 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 = 6 or a = 3
If a = 6 and b = 9 - 6 = 3 them the equation of the line is.
=> x/6 + y/3 = 1
=> x + 2y / 6 = 1
=> x + 2y = 6
=> x + 2y - 6 = 0
If a = 3 and b = 9 - 3 = 3 them the equation of the line is.
=> x/3 + y/6 = 1
=> 2x + y / 6 = 1
=> 2x + y = 6
=> 2x + y - 6 = 0
Hence, the equation of a line is x + 2y - 6 = 0 and 2x + y - 6 = 0.