Circle And System Of Circles Question 137
Question: Middle point of the chord of the circle $ x^{2}+y^{2}=25 $ intercepted on the line $ x-2y=2 $ is
Options:
A) $ ( \frac{3}{5},\frac{4}{5} ) $
B) $ (-2,-2) $
C) $ ( \frac{2}{5},-\frac{4}{5} ) $
D) $ ( \frac{8}{3},\frac{1}{3} ) $
Show Answer
Answer:
Correct Answer: C
Solution:
Here the intersection point of chord and circle can be found by
Solving the equation of circle with the equation of given line,
therefore, the points of intersection are (-4, -3) and $ ( \frac{24}{5},\ \frac{7}{5} ) $ .
Hence the midpoint is $ ( \frac{-4+\frac{24}{5}}{2},\ \frac{-3+\frac{7}{5}}{2} )=( \frac{2}{5},\ -\frac{4}{5} ) $ .
BETA
