Conic Sections Question 74
Question: If the straight line $ x+y=1 $ touches the parabola $ y^{2}-y+x=0 $ , then the co-ordinates of the point of contact are
[RPET 1991]
Options:
A) (1, 1)
B) $ ( \frac{1}{2},\ \frac{1}{2} ) $
C) (0, 1)
D) (1, 0)
Show Answer
Answer:
Correct Answer: C
Solution:
m of tangent $ =-1 $ . Also from equation of parabola, we get gradient at $ (h,k) $ as the slope of parabola $ =\frac{dy}{dx}=\frac{-1}{2y-1}=\frac{-1}{2k-1} $
Since line and parabola touch at $ (h,k) $
therefore $ \frac{-1}{2k-1}=-1 $
therefore $ -2k+1=-1 $
therefore $ k=1 $
Putting this value in $ x+y=1 $ , we have $ h=0, $ so the point of contact is $ (0,1). $
BETA
