Problem 1 :
Find the equation of the line passing through (22, -6) and having intercept on x-axis exceeds the intercept on y-axis by 5.
Solution :
x-intercept(a) = b + 5, y -intercept = b
(x/a) + (y/b) = 1
x/(b+5) + y/b = 1
The straight line is passing through the point (22, -6)
22/(b+5) - 6/b = 1
22b - 6(b + 5) = b(b + 5)
22b - 6b - 30 = b2 + 5b
16b - 30 = b2 + 5b
b2 + 5b - 16b + 30 = 0
b2 - 11b + 30 = 0
(b - 5)(b - 6) = 0
b - 5 = 0 ==> b = 5 a = 5+5 = 10 ==> a = 10 x/a + y/b = 1 x/10 + y/5 = 1 (x + 2y)/10 = 1 x - 2y = 10 x + 2y - 10 = 0 |
b - 6 = 0 ==> b = 6 a = 6 + 5 = 11 ==> a = 11 x/a + y/b = 1 x/11 + y/6 = 1 (6x + 11y)/66 = 1 6x + 11y = 66 6x + 11y - 66 = 0 |
Problem 2 :
If A (3, 6) and C (-1, 2) are two vertices of a rhombus ABCD, then find the equation of straight line that lies along the diagonal BD.
Solution :
In any rhombus diagonals bisect each other at right angle.
In any rhombus midpoint of the diagonals will be equal.
Midpoint of AC = Midpoint of BD
Midpoint of AC = ((x1 + x2)/2, (y1 + y2)/2)
= ((3 + (-1))/2, (6 + 2)/2)
= (2/2, 8/2)
= (1, 4)
(1, 4) is a point lies of the diagonal BD.
Slope of AC x Slope of BD = -1
Slope of AC :
m = (y2 - y1)/(x2 - x1)
= (2 - 6)/(-1 - 3)
= -4/(-4)
= 1
Slope of BD :
Slope of BD = -1/1 ==> -1
Equation of BD :
(y - y2) = m(x - x1)
y - 4 = -1(x - 1)
y - 4 = -x + 1
x + y - 4 - 1 = 0
x + y - 5 = 0
Hence the required equation is x + y - 5 = 0.
Problem 3 :
Find the equation of the line whose gradient is 3/2 and which passes through P, where P divides the line segment joining A(-2, 6) and B (3, -4) in the ratio 2 : 3 internally.
Solution :
First we need to find the point P.
P = (lx2 + mx1)/(l + m), (ly2 + my1)/(l + m)
p = (2(3) + 3(-2))/(2+3), (2(-4) + 3(6))/(2+3)
= (6 -6)/5, (-8 + 18)/5
= 0/5, 10/5
= (0, 2)
(x1, y1) ==> (0, 2) m = 3/2
(y - y2) = m(x - x1)
(y - 2) = (3/2)(x - 0)
2(y - 2) = 3x
2y - 4 = 3x
3x - 2y + 4 = 0
Hence the required equation is 3x - 2y + 4 = 0.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 17, 24 11:27 PM
Apr 16, 24 09:28 AM
Apr 15, 24 11:17 PM