Straight Line Question 227
Question: Let $ (h,k) $ be a fixed point where $ h>0,k>0. $ A straight line passing through this point cuts the positive direction of the coordinate axes at the points P and Q. Then the minimum area of the $ \Delta OPQ.O $ O being the origin, is
Options:
A) 4hk sq. units
B) 2hk sq. units
C) 3hk sq. units
D) None of these
Correct Answer: B $ =\frac{1}{2}\frac{(mh-k)(k-mh)}{m} $ $ \Rightarrow 2mS=hkm-k^{2}-h^{2}m^{2}+khm $ $ \Rightarrow h^{2}m^{2}-2(hk-S)m+k^{2}=0 $
Since, m is real $ \therefore 4{{(hk-S)}^{2}}-4h^{2}k^{2}\ge 0 $ $ \Rightarrow S-2hk\ge 0\Rightarrow S\ge 2hk $
Hence, minimum value of S is 2hk sq. units.Show Answer
Answer:
Solution:
$ \therefore $ its discriminant $ D\ge 0 $
BETA
