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10-1.Circle and System of Circles
hard
ઉગમબિદુમાંથી વર્તૂળ ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ પર દોરવામાં આવેલ સ્પર્શકનું સમીકરણ મેળવો.
A
$x = 0,y = 0$
B
$({h^2} - {r^2})x - 2rhy = 0,x = 0$
C
$y = 0,x = 4$
D
$({h^2} - {r^2})x + 2rhy = 0,x = 0$
(IIT-1988)
Solution
(b) The equation of tangents is $S{S_1} = {T^2}$
$ \Rightarrow {h^2}({x^2} + {y^2} – 2rx – 2hy + {h^2})$
$= {(rx + hy – {h^2})^2}$
$\Rightarrow ({h^2} – {r^2}){x^2} – 2rhxy = 0 $
$\Rightarrow x\{ ({h^2} – {r^2})x – 2rhy\} = 0$
$ \Rightarrow x = 0,\;({h^2} – {r^2})x – 2rhy = 0$.
Standard 11
Mathematics
