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```
Can you help solve this problem? Q. Prove the locus of the centre of the circle 1/2(x*x+y*y) +xcosa + ysina -4 =0 is x*x+y*y=1

```
9 years ago

```							1/2(x2+y2) + xcosa + ysina - 4 = 0
x2+y2 + 2xcosa + 2ysina - 8 =0
coordinates of center = (h,k) = (-g,-f)
g = cosa , f=sina             (from eq of circle)
(h,k) = (-cosa, -sina)
h = -cosa , k = -sina
h2 + k2 = (-cosa)2 + (-sina)2
=sin2a+cos2a=1
h2 + k2 = 1
replacing (h,k) by (x,y)
x2+y2 = 1
this is the required equation
approve my ans if u like it
```
9 years ago
```							Let center of the circle be (h, k) .
center of given circle=(-cos a, -sin a)
(-cos a, -sin a) =(h, k) → h = cos a and k = -sin a
cos2a + sin2a = 1 → h2+k2= 1
locus of (h,k) is x2+y2=1
```
9 years ago
```							Thank you sirs.
```
9 years ago
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