If y
= 2x + K is a diameter to the circle
2(x² + y) + 3x + 4y – 1 = 0, then K equals​

Question

If y
= 2x + K is a diameter to the circle
2(x² + y) + 3x + 4y – 1 = 0, then K equals​

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Ruby 2 months 2021-07-27T23:22:58+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-27T23:24:53+00:00

    Answer:

    1/2

    Step-by-step explanation:

    Consider the given equation of the circle.

    2(x  

    2

    +y  

    2

    )+3x+4y−1=0

    x  

    2

    +y  

    2

    +  

    2

    3

    ​  

    x+2y−  

    2

    1

    ​  

    =0

    General equation of circle is,

    x  

    2

    +y  

    2

    +2gx+2fy+c=0

    Therefore,

    2g=  

    2

    3

    ​  

    ⇒g=  

    4

    3

    ​  

     

    2f=2⇒f=1

    c=−  

    2

    1

    ​  

     

    We know that centre of the circle,

    C(−g,−f)

    C(−  

    4

    3

    ​  

    ,−1)

    Since, the diameter of this circle is,

    y=2x+k

    Therefore, the centre of this circle lies on the diameter,

    −1=2×−  

    4

    3

    ​  

    +k

    −1=−  

    2

    3

    ​  

    +k

    k=  

    2

    1

    ​  

     

    Hence, the value of k is  

    2

    1

    ​  

    .

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