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Rohit G Grade: 11
        


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


6 years ago

Answers : (3)

vikas askiitian expert
510 Points
										

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

6 years ago
ANAM V. RANGA REDDY
24 Points
										

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

6 years ago
Rohit G
31 Points
										

Thank you sirs. 

6 years ago
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