Conic Sections Question 104
Question: The equation of the tangent to the parabola $ y^{2}=9x $ which goes through the point (4, 10), is
[MP PET 2000]
Options:
A) $ x+4y+1=0 $
B) $ 9x+4y+4=0 $
C) $ x-4y+36=0 $
D) $ 9x-4y+4=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that $ y^{2}=9x $ . Here, $ a=\frac{9}{4} $ . Now, equation of tangent to the parabola $ y^{2}=9x $ is $ y=mx+\frac{9/4}{m} $
If this tangent goes through the point $ (4,10), $ then $ 10=4m+\frac{9}{4m} $
$ \Rightarrow (4m-9)(4m-1)=0 $
$ \Rightarrow m=\frac{9}{4},\frac{1}{4} $
Equation of tangents are, $ 4y=x+36 $
and $ y=-2x-k $
or $ x-4y+36=0 $ and $ 9x-4y+4=0 $ .
BETA
