A) (-8/5, 2)
B) (-5/8, 1/2)
C) (1/2, 5/8)
D) (5/8, -1/2)
Correct Answer: B
Solution :
Given equation of parabola written in standard form, we get \[4{{\left( y-\frac{1}{2} \right)}^{2}}=6(x+1)\Rightarrow {{\left( y-\frac{1}{2} \right)}^{2}}=\frac{3}{2}(x+1)\Rightarrow {{Y}^{2}}=\frac{3}{2}X\] where, \[Y=y-\frac{1}{2},\,\,X=x+1\] \[\therefore y=Y+\frac{1}{2},\,\,\,x=X-1\] ?..(i) For focus \[X=a,\,\,Y=0\] \[\because 4a=\frac{3}{2}\Rightarrow a=\frac{3}{8}\Rightarrow x=\frac{3}{8}-1=-\frac{5}{8}\] \[y=0+\frac{1}{2}=\frac{1}{2}\], Focus\[=\left( -\frac{5}{8},\frac{1}{2} \right)\].
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