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Question

If y=2x+K is a diameter to the circle 2(x2+y2)+3x+4y−1=0, then K equals

A
0
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B
1
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C
2
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D
12
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Solution

The correct option is C 12

Consider the given equation of the circle.

2(x2+y2)+3x+4y1=0

x2+y2+32x+2y12=0

General equation of circle is,

x2+y2+2gx+2fy+c=0

Therefore,

2g=32g=34

2f=2f=1

c=12

We know that centre of the circle,

C(g,f)

C(34,1)

Since, the diameter of this circle is,

y=2x+k

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

1=2×34+k

1=32+k

k=12

Hence, the value of k is 12.


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