Question

If the line $ y=7x-25 $ meets the circle $ {{x}^{2}}+{{y}^{2}}=25 $ in the points A, B then the distance between A and B is

• A. $ \sqrt{10} $
• B. $ 10 $
• C. $ 5\sqrt{2} $
• D. $ 5 $

Answer 1

Answer: (C)

The intersection point of line $ y=7x-25 $ and circle
$ {{x}^{2}}+{{y}^{2}}=25 $ is $ {{x}^{2}}+{{(7x-25)}^{2}}=25 $
$ \Rightarrow $ $ 50{{x}^{2}}-350x+600=0 $
$ \Rightarrow $ $ {{x}^{2}}-7x+12=0 $
$ \Rightarrow $ $ (x-3)(x-4)=0 $
$ \Rightarrow $ $ x=3,\,x=4 $ and $ y=-4,3 $
$ \therefore $ Coordinates of $ A(3,-4) $ and $ B(4,3) $
$ \therefore $ Length, $ AB=\sqrt{{{(4-3)}^{2}}+{{(3+4)}^{2}}} $
' $ =\sqrt{1+49}=5\sqrt{2} $