Question

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

Answer 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

​  

.