Straight Line Question 260
Question: If the sum of the squares of the distances of the point (x, y) from the pints (a, 0) and (-a, 0) is $ 2b^{2}, $ then which one of the following is correct?
Options:
A) $ x^{2}+a^{2}=b^{2}+y^{2} $
B) $ x^{2}+a^{2}=2b^{2}-y^{2} $
C) $ x^{2}-a^{2}=b^{2}+y^{2} $
D) $ x^{2}+a^{2}=b^{2}-y^{2} $
Correct Answer: D $ \therefore PA^{2}+PB^{2}=2b^{2} $ $ {{(x-a)}^{2}}+{{(y-0)}^{2}}+{{(x+a)}^{2}}+{{(y-0)}^{2}}=2b^{2} $ $ \Rightarrow x^{2}+a^{2}-2ax+y^{2}+x^{2}+a^{2}+2ax+y^{2}=2b^{2} $ $ \Rightarrow x^{2}+a^{2}+y^{2}=b^{2} $ $ \Rightarrow x^{2}+a^{2}=b^{2}-y^{2} $
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Answer:
Solution:
BETA
