Triangle oab is formed by the lines x^2-4x*y+y^2=0 and the line ab,the equation of line ab is 2*x+3*y-1=0.find the equation of the median of the triangle drawn from the origin
Answers
Given : Triangle oab is formed by the lines x²-4x*y+y²=0 and the line ab 2x+3y-1=0
To find : the equation of the median of the triangle drawn from the origin
Solution:
x²-4x*y+y²=0
2x + 3y - 1 = 0
=> 2x = 1 - 3y
=> 4x² = 1 + 9y² - 6y
x²-4x*y+y²=0
=> 4x²-16x*y+4y²=0
=> 1 + 9y² - 6y - 8(1 - 3y) y + 4y²=0
=> 37y² - 14y + 1 = 0
=> y1 + y2 = 14/37 ( y1 & y2 are the two points where lines intersecting)
Hence (y1 + y2)/2 is y coordinate of median
(y1 + y2)/2 = 7/37
2x = 1 - 3y
=> 2x = 1 - 3(7/37)
=> 2x = 16/37
=> x = 8/37
Median = 8/37 , 7/37
Origin = 0 , 0
Slope = 7/8
y - 0 = (7/8)(x - 0)
=> 8y = 7x
=> 7x - 8y = 0
7x - 8y = 0 is the Equation the median of triangle drawn from the origin
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Answer:
Hey mate
Given : Triangle oab is formed by the lines x²-4x*y+y²=0 and the line ab 2x+3y-1=0
To find : the equation of the median of the triangle drawn from the origin
Solution:
x²-4x*y+y²=0
2x + 3y - 1 = 0
=> 2x = 1 - 3y
=> 4x² = 1 + 9y² - 6y
x²-4x*y+y²=0
=> 4x²-16x*y+4y²=0
=> 1 + 9y² - 6y - 8(1 - 3y) y + 4y²=0
=> 37y² - 14y + 1 = 0
=> y1 + y2 = 14/37 ( y1 & y2 are the two points where lines intersecting)
Hence (y1 + y2)/2 is y coordinate of median
(y1 + y2)/2 = 7/37
2x = 1 - 3y
=> 2x = 1 - 3(7/37)
=> 2x = 16/37
=> x = 8/37
Median = 8/37 , 7/37
Origin = 0 , 0
Slope = 7/8
y - 0 = (7/8)(x - 0)
=> 8y = 7x
=> 7x - 8y = 0
7x - 8y = 0 is the Equation the median of triangle drawn from the origin
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