Pair Of Straight Lines Question 134
Question: The equation of the pair of straight lines parallel to x-axis and touching the circle $ x^{2}+y^{2}-6x-4y-12=0 $
[Kerala (Engg.) 2002]
Options:
A) $ y^{2}-4y-21=0 $
B) $ y^{2}+4y-21=0 $
C) $ y^{2}-4y+21=0 $
D) $ y^{2}+4y+21=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the lines are $ y=m_1x+c_1 $ and $ y=m_2x+c_2 $.
Since pair of straight lines parallel to x-axis, $ m_1=m_2=0 $ and the lines will be $ y=c_1 $ and $ y=c_2 $
Given circle is $ x^{2}+y^{2}-6x-4y-12=0 $ , centre (3, 2) and radius = 5.
Here, the perpendicular drawn from centre to the lines are CP and $ C{P}’ $ . $ CP=\frac{2-c_1}{\sqrt{1}}=\pm 5 $
Therefore $ 2-c_1=\pm 5 $
$ c_1=7 $ and $ c_1=-3 $
Hence the lines are $ y-7=0,y+3=0 $ i.e., $ (y-7)(y+3)=0 $
Pair of straight lines is $ y^{2}-4y-21=0 $ .
BETA
