#### Thank you for registering.

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

Click to Chat

1800-1023-196

+91-120-4616500

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

# The value of​ λ for which the circle x2+y2-3x+λy-5=0 and 4(x2+y2)-12x-y-9=0becomes concentric is

Ram Kushwah
108 Points
3 months ago
The eqn of second cicle is:

4(x²+y²)-12x-y-9=0
4x²+4y²-12x-y=9
x² + y² -3x – y/4 = 9/4
(x²-3x+9/4) +(y²-y/4+1/64)=9/4+9/4+1/64
(x-3/2)²+(y-1/8)² =289/64
Or (x-3/2)²+(y-1/8)² =(17/8)²
Thus the centre of this circle is ( 3/2,1/8)
Now the eqn of first cicle is:
x²+y²-3x+λy-5=0
This can be written as
x²-3x+y²+λy=5
{x²-3x+(9/4) }+(y²+λy+λ²/4)=5+9/4+λ²/4
or  (x-3/2)² +(y+λ/2)²=(29+λ²)/4
Centre of this cicle is (3/2,-λ/2)
For both the circles to be concentric the
centres should be same

Thus both the following centres are same

(3/2,1/8) and (3/2,-λ/2)

On comparision we get

-λ/2 =1/8

λ=-2/8=-1/4