Question

Two circles, each radius $5$, have a common tangent at $(1,1)$ whose equation is $3x+4y-7=0$. Then their centre are:

• A. $(4,-5),(-2,3)$
• B. $(4,-3),(-2,5)$
• C. $(4,5),(-2,-3)$
• D. $Noneofthese$

Answer 1

The correct option is C $(4,5),(-2,-3)$

REF.Image

radius = 5

tangent (1,1)

$e{q}^n$ is $3x+4y-7=0$

$e{q}^n$ of tangent, $3x+4y-7=0$

$y=\frac{-3}{4}x+\frac{7}{4}$

$m=\frac{-3}{4}$

slope of a normal line = $\frac{+4}{3}$

here the radius is 5

Here, $x=3,y=4$

$(x,y)=(-2,-3),(4,5)$

are the centres.