Equation of the Line When Parallel Line and Sum of Intercepts is Given :
Here we are going to see how to find the equation of the line when parallel line and sum of intercepts is given.
Question 1 :
Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15
Since the required line is parallel to the line 2x + 3y = 10
Equation of the required line will be in the form
2x + 3y + k = 0
Let us change the above equation to intercept form.
2x + 3y = -k
2x/(-k) + 3y/(-k) = 1
x/(-k/2) + y/(-k/3) = 1
x -intercept = a and y -intercept = b
Sum of intercepts = 15
a + b = 15
(-k/2) + (-k/3) = 15
(-3k - 2k)/6 = 15
-5k/6 = 15
k = -15(6)/5 = -18
2x + 3y - 18 = 0
Hence the equation of the required line is 2x + 3y - 18 = 0.
Question 2 :
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10,−2) to the line x + y − 2 = 0
The lines PQ and AB are perpendicular to each other.
Equation of AB :
x + y - 2 = 0
Equation of PQ :
x - y + k = 0
The point P (-10, -2) lies on the line PQ.
-10 + 2 + k = 0
k - 8 = 0
k = 8
Equation of PQ is x - y + 8 = 0
By solving the equations of AB and PQ, we get the value of P.
x + y - 2 = 0 ----(1)
x - y + 8 = 0 ----(2)
(1) + (2) ==> 2x + 6 = 0 ==> x = -3
By applying the value of x in (1), we get the value of y.
-3 + y - 2 = 0
-5 + y = 0
y = 5
Hence the required point P (-3, 5)
Length of perpendicular :
= √(x2 - x1)2 + (y2 - y1)2
= √(-3+10)2 + (5+2)2
= √72 + 72
= √98 = 7√2 units
After having gone through the stuff given above, we hope that the students would have understood "Equation of the Line When Parallel Line and Sum of Intercepts is Given".
Apart from the stuff given above, if you want to know more about "Equation of the Line When Parallel Line and Sum of Intercepts is Given". Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
Customary units worksheet
Integers and absolute value worksheets
Nature of the roots of a quadratic equation worksheets
Point of intersection
MATH FOR KIDS
Word problems on linear equations
Trigonometry word problems
Word problems on mixed fractrions
Converting repeating decimals in to fractions