Conic Sections Question 16
Question: The focus of the parabola $ x^{2}=2x+2y $ is
Options:
A) $ ( \frac{3}{2},\ \frac{-1}{2} ) $
B) $ ( 1,\ \frac{-1}{2} ) $
C) (1, 0)
D) (0, 1)
Show Answer
Answer:
Correct Answer: C
Solution:
The parabola is $ x^{2}-2x=2y $
or $ x^{2}-2x+1=2y+1 $
therefore $ {{(x-1)}^{2}}=2( y+\frac{1}{2} ) $
Here $ 4a=2\Rightarrow a=\frac{1}{2} $
Now focus is $ ( x-1=0,y+\frac{1}{2}=\frac{1}{2} )i.e.,(1,0) $ .
BETA
