Q11 and Q13 - Week 3 :Graded

[Dnemises .s]

Dear Team ,

 (r+5)x–(r–1)y+r2+4r−5=0

reduces to 

(r+5) x - (r - 1)y + (r+5)(r-1) =0

which implies that  at r = -5 or r= 1  reduce the equation as Y=0 and X=0 respectively 

Y=0 is equation of X-axis itself ..  can it be considered as parallel to X- axis?

Similarly,

X=0 is equation of Y-axis itself... can be considered as parallel to Y- axis?

Thanks

[Hemant Sharma]

how can you say (r+5)x-(r-1)y+(r+5)(r-1)=0 implies that r=-5 or 1

it is not linear equation in one variable, it is linear equation in two variables i.e. fow every value of x there will be a value of y
it is not like r can be only -5 & 1, it can be any number as it is a variable. but for every new value of r it will make the equation to be an equation of a different line. 

I think you can solve the question by comparing the slope of this line and the targeted line. 

p.s- correct me if i am wrong (i am a learner and there are few speculations). 

Thank You 

[nee...@gmail.com]

To make the equation parallel to x-axis you have to make its slope 0. From the 'general equation form' slope is -A/B. Which means (r+5)/(r-1) = 0, it will give you the r value as -5. same way you have to calculate the value of r for which equation will be parallel to y-axis.

[Shesh S]

I believe that u cannot have any value of r in Real that can make this line parallel to X-axis or Y-axis. Because of the following reasons -

a) Lets CONTRADICT  that  r= -5 or r= 1 is a solution 

- putting r = -5 would give you 0.x - 4.y +0 = 0  or  Y=0 --- Please note that this line is not equal parallel to X-axis ! This line is X-axis itself 

In general you cant say that a line "L" is parallel to itself - Parallel mean they dont intersect at a defined point, Whereas the same line intersect itself at everypoint 

- putting r =1 similarly would give x =0

b) In general any line of form a.x +/-  b.Y +/- a.b =0 can never be parallel to X or Y axis for any value of a or b 

as it can be written as (x/b)+(y/a) = +/- 1

having intercept at b and a 

put  a = (r-5) 

and b =  (r -1)

you would get the above equation 

c) Also in general , I believe that there has to be a more solid logic ( not mere allocation of marks) to believe that something is right