Week 3 - Graded Assignment 3 - Q13 - Solution - Doubt

[Zohair Merchant]

Q13) Find the values of rr for which the line (r+5)x–(r–1)y+r2+4r−5=0(r+5)x–(r–1)y+r2+4r−5=0 is parallel to the y-axis

The Solution mentions:

"Since line ` is parallel to the Y -axis (x = 0), using parallel line condition, we have

a1b2 = a2b1

where a1 = 1, b1 = 0, a2 = r + 5, b2 = −(r − 1) = 1 − r,

=⇒ 1 − r = 0

Hence r = 1."

Doubt:

How did we find the values of a1 and b1,  as a1 = 1 and b1 = 0?

[Anand Iyer]

Equation of Y-axis is x = 0 ==> 1x + 0y + 0c = 0

From this, a1 = 1, b1 -= 0, c1 = 0

[Zohair Merchant]

Also Problem Solving tips mentions:

"• Given two straight lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where b1, b2 not = 0,

– The lines are parallel to each other, if a1 × b2 = a2 × b1."

Here they've said b1, b2 not equal to 0 means both simultaneusly or separately?

If separately one of the shouldn't be 0, then how can the above solution have b1=0?

On Wednesday, November 11, 2020 at 12:28:29 PM UTC+5:30 Zohair Merchant wrote:

[Debajyoti Biswas]

Zohair, parallel line to y axis will have infinite slope. So (r+5)/(r-1)=infinity. Now how to do this? by taking r-1=0 or r=1

[sareena sanil]

by taking r-1=0 correct?