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consider a family of circles passing through two fixed points `S(3,7)` and `B(6,5)`. If the common chords of the circle `x^(2)+y^(2)-4x-6y-3=0` and the members of the family of circles pass through a fixed point (a,b), thenA. `a+3b=25`B. `3b-a=21`C. `3a+b=25`D. `3a-b=21` |
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Answer» Correct Answer - A::B Family of circle `S+lamdaL=0` `S_(1)-=(x-3)(x-6)+(y-7)(y-5)+lamda(2x+3-27)=0` `x^(2)+y^(2)+x(2lamda-9)+y(3lamda-12)+(53-27lamda)=0` common chord of family of circle and given circle is `S_(1)-S_(2)` `=0(S_(22)` given circle) `(-5x-6y+56)+lamda(2x+3y-27)=0` Which represents family of lines passing through the point `(2,(23)/(3))impliesa=2,b=(23)/(3)` |
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