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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


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


Grade:11

3 Answers

vikas askiitian expert
509 Points
10 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

ANAM V. RANGA REDDY
24 Points
10 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

Rohit G
31 Points
10 years ago

Thank you sirs. 

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