A) \[{{x}^{2}}+{{y}^{2}}=4\]
B) \[{{x}^{2}}+{{y}^{2}}=16\]
C) \[{{x}^{2}}+{{y}^{2}}=8\]
D) \[|x|+|y|=8\]
Correct Answer: B
Solution :
Let the line segment whose length is 8 unit intercept the coordinate axes at \[A(a,0)\] and \[B(0,b)\] x-axes and y-axes respectively. Let \[P(h,k)\] be the mid-point of line segment AB. \[\Rightarrow \] \[h=a/2\] and \[k=b/2\] \[\Rightarrow \] \[a=2\,h\]and \[b=2k\] ?..(i) Now, \[AB=\sqrt{{{(a-0)}^{2}}+{{(b-0)}^{2}}}\] \[A{{B}^{2}}={{a}^{2}}+{{b}^{2}}\] \[\Rightarrow \] \[{{(8)}^{2}}={{(2h)}^{2}}+{{(2k)}^{2}}\] (from Eq. (i)] \[\Rightarrow \] \[{{h}^{2}}+{{k}^{2}}=16\] \[\therefore \] The leocus of mid-point P is \[{{x}^{2}}+{{y}^{2}}=16\]You need to login to perform this action.
You will be redirected in
3 sec