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Consider the family of circles : x^(2)+y...

Consider the family of circles : `x^(2)+y^(2)-3x-4y-c_(i)=0, c_(i)inN`
`(i=1,2,3,…,n)`
Also, let all circles intersects X-axis at integral points only and `c_(1)ltc_(2)ltc_(3)ltc_(4)…ltc_(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)-3x-4y-(c_(2)-c_(1))=0` and circle `x^(2)+y^(2)=r^(2)` have only one common tangent, then

A

A) `r=1//2`

B

B) tangent passes through `(10,0)`

C

C) (3, 4) lies outside the circle `x^(2)+y^(2)=r^(2)`

D

D) `c_(2)=2r+c_(1)`

Text Solution

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The correct Answer is:
D
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