Consider the family of circles: \( x^{2}+y^{2}-3 x-4 y-c_{i}=0, c_{i} \in N \) \( (i=1,2,3, \ldo... VIDEO
Consider the family of circles: \( x^{2}+y^{2}-3 x-4 y-c_{i}=0, c_{i} \in N \) \( (i=1,2,3, \ldots, n) \)
Also, let all circles intersects \( X \)-axis at integral points only and \( c_{1}c_{2}c_{3}c_{4} \ldotsc_{n} \). A point \( (x, y) \) is said to be integral point, if both coordinates \( x \) and \( y \) are integers.
If circle \( x^{2}+y^{2}-3 x-4 y-\left(c_{2}-c_{1}\right)=0 \) and circle \( x^{2}+y^{2}=r^{2} \) have only one common tangent, then (a) \( r=1 / 2 \)
(b) tangent passes through \( (10,0) \)
(c) \( (3,4) \) lies outside the circle \( x^{2}+y^{2}=r^{2} \)
(d) \( c_{2}=2 r+c_{1} \)
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