#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# Can you help solve this problem?Q. Prove the locus of the centre of the circle1/2(x*x+y*y) +xcosa + ysina -4 =0 is x*x+y*y=1

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

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