Question

Intersection points of the circles $ {{x}^{2}}+{{y}^{2}}=25 $ and $ {{x}^{2}}+{{y}^{2}}-8x+7=0, $ are

• A. $(4, 3)$ and $ (4,-3) $
• B. $ (4,-3) $ and $ (-4,-3) $
• C. $ (-4,3) $ and $(4, 3)$
• D. $(4, 3)$ and $(3, 4)$

Answer 1

Answer: (A)

Given, $ {{x}^{2}}+{{y}^{2}}=25 $ ...(i) and $ {{x}^{2}}+{{y}^{2}}-8x+7=0 $ ...(ii)
From Eqs. (i) and (ii), $ 25-8x+7=0 $ $ \Rightarrow $ $ 8x=32 $ $ \Rightarrow $
$ x=4 $ and $ y=\pm 3 $
Hence, intersection points are (4,3) and $ (4,-3) $ .