# Math

A straight line x/a -y/b =1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of coordinates .find the equation of straight line

1. 👍 0
2. 👎 0
3. 👁 250
1. since (8,6) lies on it,
8/a - 6/b = 1
(8b - 6a)/(ab) = 1
8b - 6a = ab
8b - ab = 6a
b(8 - a) = 6a
b = 6a/(8-a) **

x/a - y/b = 1 is in the intercept form, that is
the x-intercept is (a,0)
the y-intercept is (0,b)
so the area of the triangle is (1/2)(ab)
(1/2)(ab) = 12
ab = 24 ***

sub ** into ***
a(6a)/(8-a) = 24
6a^2 = 192 - 24a
a^2 + 4a - 32 = 0
(a+8)(a-4) = 0
a = -8 or a = 4

if a = 4, b = 6
x/4 - y/6 = 1 ---> 6x - 4y = 24 or 3x - 2y = 12

if a = -8, b = -3
x/-8 - y/-3 = 1 ---> -3x + 8y = 24 or 3x - 8y = -24

1. 👍 3
2. 👎 0
posted by Reiny
2. Very useful

1. 👍 1
2. 👎 0
posted by Amar

## Similar Questions

1. ### Math

This question concerns the straight line that passes through the points (−1, 3) and (2, −6). Choose the three true statements from the following. Options A The gradient of the line is 3. B The gradient of the line is −3. C

asked by S Rey on June 5, 2010
2. ### Mathamatics

This question concerns the straight line that passes through the points (−1, 3) and (2, −6). Choose the three true statements from the following. Options A) The gradient of the line is 3. B) The gradient of the line is −3.

asked by S Rey on June 6, 2010
3. ### Equation of a straight line.

1. Find the equation of the line described in each case: a) Gradient 3, cuts through (0, 6). b) Steepness of 4, passes through (0, -2). c)Parallel to y = 5x - 1, cuts the y-axis at (0, 10). d)Cuts through (0, 7) and (5, 17) 2.

asked by DJ Frankie Pigeon on January 15, 2007
4. ### Straight Lines

The axes being inclined at an angle of 30°, find the equation to the straight line which passes through the point(-2,3) and is perpendicular to the straight line y + 3x = 6

asked by Kewal on January 21, 2012
5. ### Calculus

I asked for help on a question yesterday and I got really good help and I was wondering if someone could help with this problem too. This is the question: Find an equation of the line through the point (1,3) that cuts off the

asked by Kristal on November 12, 2006
6. ### Math

(a) Straight line passes through the point (-2,8) and is parallel to the line x+2y=4 Slope Intercept Equation is: (b) Straight line passes through the point (-1,9) and is perpendicular to the line 5x+y=4 Slope Intercept Equation

asked by Yin on April 12, 2015
7. ### math

A straight line is the shortest distance between two points. In a triangle, the sum of two sides of the triangle is greater than the third side. Also, a perpendicular drawn from a point to a line is the shortest distance from the

asked by peter on May 15, 2014
8. ### maths

find the equation to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=0

asked by Anonymous on January 10, 2013
9. ### calculus HELP URGENT

Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.

asked by Santha on March 16, 2010
10. ### Calculus

PLEASE HELP Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.

asked by Santha on March 16, 2010

More Similar Questions