I’m getting both B and D options

# Circles

If u r getting B then D is impossible

Is the ans D?

in both books key is given B and D respectively

it’s PYQ mains

even diff websites have their diff explanations

which year bro

2009

D makes more sense to me by the method u followed. For cases where u get lambda as 0 or infinite don’t eliminate the denominator. I mean if it’s S1+mS2 and you get m as infinite then that means you have to consider only S2=0. Now S2 will obviously pass thru P n Q so see about 1,1 . By putting 1,1 if u do not get real value of p then you can eliminate the denominator for which lambda came out infinite

Follow same case for S1

But I would say a better method will be finding out common chord S1-S2 =0. P n Q will lie on this chord so check for 1,1 as circle doesn’t pass thru collinear pts.

x+5y+p^2+2p-5 =0 (1,1)

p^2+2p+2=0 no real values of p.

Got it Bro, thanks a lot!!!

Bro ig it’ll be p^2+2p+1=0

So p will have 2 equal real values!

I’m totally confused now

Ohh then p=/ -1 so ig option A must be the ans. Just saw p=/ -1 is also given on internet. This method is definitely right bro. I think the mistake in urs is ur only checking whether lambda is defined or not. But that just accounts for 1 case. Another case is when lambda is not -1 as the circle itself is undefined. For this case, put 1,1 and see which value gives lambda as -1. That value is p=-1. Just a case miss.

Thanks bhavik!!

I wonder what was the official key!!!

By major seg, I suppose they mean any point on major arc right? I am getting m as±1 then. Just draw figure bro its pretty easy … y intercept is 1 and its 90* at centre so it must intersect circle again at either 1,0 or -1,0 to make it quarter circle. So acc m is ±1

In this solution they took the angle subtended by the chord at centre =45° which is wrong

Oh…yes!!!missed on that thanks Amish, Bhavik!!

Hey bro,I am getting option A.How you are getting B and D.