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Question

The equation of the pair of straight lines parallel to xaxis and touching the circle x2+y2-6x-4y-12=0


A

y24y21=0

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B

y2+4y21=0

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C

y24y+21=0

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D

y2+4y+21=0

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Solution

The correct option is A

y24y21=0


Explanation of the correct answer.

Step 1: Find the radius and the center.

Given: Equation of the circle is x2+y2-6x-4y-12=0

comparing with ax2+by2+2gx+2fy+c=0

a=1,b=1,g=-3,f=-2,c=-12

Since the center is -ga,-fa , and the radius is 1ag2+f2-ac

Therefore,

center =3,2,

radius =11(-3)2+(-2)2+12

radius =5

Step 2: Find the equation of pair of straight line..

Since, the equation of the line parallel to x axis is y=a.

The perpendicular distance from the line to the center is the radius.

So the distance from line y-a=0 to the point 3,2 is

2-a=5

2-a=±5

2-a=5

a=-3

2-a=-5

a=7

Therefore, the equation of pair of straight line is ,

y+3y-7=0

y2-4y-21=0

Hence, Option A is the correct answer.


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