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

1 thought on “If y<br />= 2x + K is a diameter to the circle<br />2(x² + y) + 3x + 4y – 1 = 0, then K equals​”

1. 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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