Straight Line Question 229
Question: If the point $ P(x,y) $ is equidistant from points $ A(a+b,b-a) $ and $ B(a-b,a+b) $ , then
Options:
A) $ ax=by $
B) $ bx=ay $ and P ca be (a, b)
C) $ x^{2}-y^{2}=2(ax+by) $
D) None of the above
Correct Answer: B $ \Rightarrow {{[x-(a+b)]}^{2}}+{{[y-(b-a)]}^{2}} $ $ ={{[x-(a-b)]}^{2}}+{{[y-(a+b)]}^{2}} $ $ \Rightarrow {{[(x-a)-b]}^{2}}+{{[(y-b)+a]}^{2}} $ $ ={{[(x-a)+b]}^{2}}+{{[(y-b)-a]}^{2}} $ $ \Rightarrow {{[(x-a)+b]}^{2}}-{{[(x-a)-b]}^{2}} $ $ ={{[(y-b)+a]}^{2}}-{{[(y-b)-a]}^{2}} $ $ \Rightarrow 4b(x-a)=4a(y-b)\Rightarrow bx=ay $ ? (i) Also, P (a, b) satisfies the condition (i), so that P can be (a, b).
Show Answer
Answer:
Solution:
BETA
