In each of the following cases determine the equation of the

In each of the following cases, determine the equation of the line perpendicular to (u) and passing through A: A(0.5; 1.5); (u): 4x - 5y + 2 = 0; A(15; 17); (u) x = 2y + 2; A(0; 5); (u): y + 2x = 2; A(1; 1); (u): y = 3; A(1; 5); (u): y = 2x + 3; A(2; - 3); (u): y = x - 5; A(- 1; - 7); (u): 0 = 4x - 3; A(- 1: - 3); (u): y = 5x + 2.

Solution

Sol:

Any line perpendicular to ax+by+c=0 is bx-ay+k=0

here a=4 b=-5

require d line is

-5x-4y+k=0

this passes thru A(0.5,1.5)

-5(0.5)-4(1.5)+k=0

-2.5-6+k=0

k=8.5

required line is -5x-4y+8.5=0

that is 5x+4y-8.5=0

(b)

x-2y-2=0

a=1 b=-2

-2x-y+k=0

passes thru A(15,17)

put x=15 y=17

-2(15)-17+k=0

-30-17+k=0

k=47

required line is -2x-y+47=0

2x+y-47=0

Solutionc:

2x+y-2=0

a=2 b=1

x-2y+k=0

this line passes thru A(0,5)

put x=0 y=5

0-2*5+k=0

k=10

the req]uired line is

x-2y+10=0

Solutiond:

y-3=0

0x+1y-3=0

a=0 b=1

bx_ay+k=o is the required line

1x-0y+k=0

this passes thru A(1,1)

1.1-0*1+k=0

k=-1

the required eq is

x-1=0

x=1

we are asked to solve oly 4 bits or 1 quest

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