Conic Sections Question 399
Question: Consider a circle with its centre lying on the focus of the parabola $ y^{2}=2px $ such that it touches the directrix of the parabola. Then, a point of intersection of the circle and the parabola is
[IIT 1995]
Options:
A) $ ( \frac{p}{3},\ p ) $
B) $ ( \frac{p}{2},\ -p ) $
C) $ ( \frac{-p}{2},\ p ) $
D) $ ( \frac{-p}{2},\ -p ) $
Show Answer
Answer:
Correct Answer: B
Solution:
Focus of parabola $ y^{2}=2px $ is $ (p/2,0) $ ……(i) Radius of circle whose centre is $ (p/2,0) $ and touching $ x+(p/2)=0 $ is p. Equation of circle is $ {{( x-\frac{p}{2} )}^{2}}+y^{2}=p^{2} $ …..(ii) From (i) and (ii), we get the point of intersection $ ( \frac{p}{2},p ),( \frac{p}{2},-p ) $ .
BETA
