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FInd the equation of circle drawn on the intercept on diameter between the axes made by the line 3x+4y=12

FInd the equation of circle drawn on the intercept on diameter between the axes made by the line 3x+4y=12

Grade:11

1 Answers

Puneet Mittal AskiitiansExpert-IITD
22 Points
11 years ago

Hi Rahul,

The anwer is :

3x + 4y = 12 or x/4 + y/3 = 1

Thus x intercept of line 3x + 4y = 12 is a = 4

and y intercept of line 3x + 4y = 12 is b = 3

The Intercept length will be root(32 + 42) = 5

Hence Diameter of circle will be 5 , thus radius will be 5/2

Now , Mid-point of Intercept will be ( 4/2 , 3/2 ) or ( 2 , 1.5 )

Hence center point of circle is ( 2 , 1.5 ) and radius is 2.5

Thus eqn of circle will be ( x - 2 )2 + ( y - 1.5 )2  = (2.5)2

Please feel free to ask as many questions you have.

Puneet

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