Question bank/JEE Main/Mathematics

If tangent at (1,2) to the circle
$c_{1}:x^{2} + y^{2} = 5\$intersects the circle
$c_{2}:x^{2} + y^{2} = 9\ at\ A\& B$and tangents at A& B to the second
circle meet at point C, then the co-ordinates of C is;fn fcUnq (1,2) ij o`Ùk $c_{1}:x^{2} + y^{2} = 5\$
o`Ùk $c_{2}:x^{2} + y^{2} = 9\$dks fcUnq A vkSj B ij dkVrh

A(4,5)B$\left( \frac{9}{15},\frac{18}{5} \right)$C(4, -5)D$\left( \frac{9}{5},\frac{18}{5} \right)$

Show answer and solution▾

Tangent at (1,2) to the circle x^2 + y^2 =5
x+2y-5=0
chord of contact from C(h,k) to $x^{2} + y^{2} = 9$
[IMAGE] hx + ky -9 = 0
compare both equation$\frac{h}{1} = \frac{k}{2} = \frac{9}{5}$
$(h,k) \equiv \left( \frac{9}{5},\frac{18}{5} \right)$
Hindi. o`Ùk (1,2) ds fcUnq x^2 + y^2 =5 ij
lehdj.k
x+2y-5=0 gS
o`Ùk $x^{2} + y^{2} = 9$ ds fy, C(h,k) thok
[IMAGE] hx + ky -9 = 0
nksuksa dh rqYkuk djus ij $\frac{h}{1} = \frac{k}{2} = \frac{9}{5}$
$\ (h,k) \equiv \left( \frac{9}{5},\frac{18}{5} \right)$

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