Question bank/JEE Main/Mathematics

If circles $x^{2} + y^{2} = c\$with radius
$\sqrt{3}\ and\ x^{2} + y^{2} + ax + by + c = 0$with radius
[IMAGE] intersect at two points A and B. If length of AB
is $\sqrt{\mathcal{l}}$then $\mathcal{l}^{2}$is;fn$\sqrt{3}\$f= o`Ùk $x^{2} + y^{2} = c\$gS rFkk
o`Ùk$\ x^{2} + y^{2} + ax + by + c = 0$dh
f= nks fcUnqvksa A rFkk B ij izfrPNsn djrh AB

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c =3
$\frac{a^{2}}{4} + \frac{b^{2}}{4} - c = 6$
$a^{2} + b^{2} = 36$
[IMAGE] common chord (AB) = ax + by + 2c =0
mHk;fu"B thok (AB) = ax + by + 2c =0
AB = 2AM
$= 2\sqrt{3 - 1} = 2\sqrt{2}$

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx