Conic Sections Question 83
Question: If line $ x=my+k $ touches the parabola $ x^{2}=4ay $ , then $ k= $
[MP PET 1995]
Options:
A) $ \frac{a}{m} $
B) am
C) $ am^{2} $
D) $ -am^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
If we replace x by y and y by x, then the line is $ y=mx+k $ and parabola $ y^{2}=4ay $ .
Hence $ k=\frac{a}{m} $ Aliter: If $ x=my+k $ touches $ x^{2}=4ay $ , then the quadratic $ {{(my+k)}^{2}}=4ay $ will have two real and equal roots i.e., $ B^{2}-4AC=0 $ , which will give us $ k=\frac{a}{m} $ .
BETA
