Math, asked by kunjshah06peqc0v, 1 year ago

If the line x + 2by + 7 =0 is a diameter of the circle circle x^2+y^2-6x+2y =0, then find the value of b.

Answers

Answered by sanjeevk28012
20

Given :

The line equation x + 2 b y + 7 = 0 is a diameter of circle

The circle equation is  x² + y² - 6 x + 2 y = 0

To Find :

The value of b

Solution :

We know,

The standard equation of circle is  x² + y² + 2 g x + 2 f y + c = 0

And Given circle equation is  x² + y² - 6 x + 2 y = 0

Comparing we get

        2 g = - 6                and           2 f = 2

i.e        g = \dfrac{-6}{2}                            i,e    f = \dfrac{2}{2}

Or,       g = - 3                             Or,  f = 1

As , The center of any circle is ( - g , - f )

So, From g and f value , center of this circle is ( - ( - 3 ) , - 1 ) = ( 3 , - 1 )

Again

The diameter equation is x + 2 b y + 7 = 0  , This diameter must pass through center ( 3 , - 1 )

Satisfying this center on diameter equation

i.e           x + 2 b y + 7 = 0  

Or,          3 + 2 b ( - 1 ) + 7 = 0

Or,          3 - 2 b + 7 = 0

Or,           10 - 2 b = 0

∴                      b = \dfrac{10}{2}

i.e                    b = 5

So, The value of b = 5

Hence, The value of b , when given line is diameter of circle is 5  . Answer

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