Suppose that the circle x^2+y^2+2 gx+2 fy+c=0 has its centre on 2x+3y-7=0 and cuts the circles x^2+y^2-4x-6y+11=0 and x^2+y^2-10x-4y+21=0 orthogonally. Then 5g-10f+3c=

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Correct answer: D. (d) Since given equation of the circle is, x^2+y^2+2 gx+2 fy+c=0…….(i) With centre (-g ,-f ) lies on the line 2x+3y-7=0 will satisfy it 2g+3f+7=0………..(ii) Since circle (i) cuts the given circles x^2+y^2-4x-6y+11=0 and x^2+y^2-10x-4y+21=0 orthogonally so, 2g (-2 )+2f (-3 )=c+11 ⇒4g+6f+c+11=0………………..(iii) and 2g (-5 )+2f (-2 )=c+21 ⇒10g+4f+c+21=0…………….(iv) From Eqs. (iii) and (iv), we get 6g-2f+10=0.....(v) From Eq. (ii) and (v), we get 11f+11=0 ⇒f=-1 so , g=-2 ⇒c=3 ∴5g-10f+3c=-10+10+9=9. Hence, option (d) is correct.

$Suppose that the circle x^{2} + y^{2} + 2 gx + 2 fy + c = 0 has its centre on 2 x + 3 y - 7 = 0 and cuts the circles x^{2} + y^{2} - 4 x - 6 y + 11 = 0 and x^{2} + y^{2} - 10 x - 4 y + 21 = 0 orthogonally. Then 5 g - 10 f + 3 c =$

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