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10-1.Circle and System of Circles
medium
જો બે વર્તૂળો $ 2x^2 + 2y^2 -3x + 6y + k = 0$ અને $x^2 + y^2 - 4x + 10y + 16 = 0$ લંબરૂપે છેદે, તો $ k$ નું મૂલ્ય....
A
$41$
B
$14$
C
$4$
D
$0$
Solution
આપેલ વર્તુળ $\,2{x^2} + 2{y^2} – 3x + 6y + k\,\, = \,\,0\,$ અથવા
$\,{x^2} + {y^2} – \frac{3}{2}\,x + \,\,3y\,\, + \,\frac{k}{2}\,\, = \,\,0\,\,…….\,\,(i)$
અને $\,{x^2} + {y^2} – 4x\,\, + \,\,10y\,\, + \,\,16\,\, = \,\,0\,\,………\,\,(ii)$
વર્તુળ (i) અને (ii) લંબરૂપે છેદતો , $\,2{g_1}\,{g_2} + \,\,2{{{f}}_1}{{{f}}_2} = \,\,{c_1} + {c_2}$
$2\,\,\left( { – \frac{3}{4}} \right)\,\,( – 2)\,\, + \,\,2\,\,\left( {\frac{3}{2}} \right)\,\,.\,5\,\, = \,\,\frac{k}{2}\,\, + \,\,16$
$3 + 15\,\, = \,\,\frac{k}{2}\,\, + \,\,16\,\, \Rightarrow \,\,18\,\, = \,\,\frac{k}{2}\,\, + \,\,16\,\, \Rightarrow \,k\,\, = \,\,4$
Standard 11
Mathematics
