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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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Mathematics
2 months
2021-07-27T23:22:58+00:00
2021-07-27T23:22:58+00:00 1 Answers
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## Answers ( )

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

.