EQUATION OF LINE WITH A POINT AND RATIO OF INTERCEPT IS GIVEN
Example 1 :
Find the equation of the straight line passing through the point (3, 4) and has intercepts which are in the ratio 3:2.
Solution :
Intercept form :
(x/a) + (y/b) = 1
Intercepts are in the ratio 3:2
So, x-intercept (a) = 3t
y-intercept (b) = 2t
(3/3t)+(4/2t) = 1
(1/t)+(2/t) = 1
3/t = 1
3 = t
t = 3
So, x-intercept (a) = 3t = 3(3) ==> 9
y-intercept (b) = 2t = 2(3) ==> 6
(x/9)+(y/6) = 1
(2x+3y)/18 = 1
2x+3y = 18
2x+3y-18 = 0
Example 2 :
Find the equation of the straight line passing through the point (5, -3) and whose intercepts on the axes are equal in magnitude but opposite in sign.
Solution :
Intercept form :
(x/a) + (y/b) = 1
intercepts are equal in magnitude but opposite in sign.
x-intercept (a) = t
y-intercept (b) = -t
The required line is passing through the point (5,-3)
(5/t)+(-3/(-t)) = 1 ---(1)
(5/t)+(3/t) = 1
(5+3)/t = 1
8/t = 1
8 = t
t = 8
By applying the value of t in (1), we get
(x/8)+(y/(-8)) = 1
(x-y)/8 = 1
x-y = 8
x-y-8 = 0
Example 3 :
Find the equation of the straight lines passing through the point (2, 2) and sum of the intercepts is 9.
Solution :
Intercept form :
(x/a) + (y/b) = 1
Sum of intercept = 9
a+b = 9
b = 9-a
The required line is passing through the point (2, 2)
(2/a)+2/(9-a) = 1
[2(9-a)+2a]/[a(9-a)] = 1
[18-2a+2a]/9a-a2 = 1
18/(9a-a2) = 1
18 = 9a-a2
a2-9a+18 = 0
(a-3) (a-6) = 0
a = 3 and a = 6
|
If a = 3 b = 6 |
If a = 6 b = 3 |
Equation of the line when a = 3 and b = 6 :
(x/3)+(y/6) = 1
(2x+y)/6 = 1
2x+y = 6
2x+y-6 = 0
Equation of the line when a = 6 and b = 3 :
(x/6)+(y/3) = 1
(x+2y)/6 = 1
x+2y = 6
x+2y-6 = 0
So, the required equations are
2x+y-6 = 0 or x+2y-6 = 0
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Internal and External Tangents of a Circle
Jan 22, 21 10:15 AM
Internal and External Tangents of a Circle
-
Volume and Surface Area of Composite Solids Worksheet
Jan 20, 21 10:31 AM
Volume and Surface Area of Composite Solids Worksheet
-
Combination of Solid Shapes Problems
Jan 20, 21 09:46 AM
Combination of Solid Shapes Problems
