#### 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

# Centre of a circle which is orthogonal to the circle x^2+y^2=25 and (x-7)^2+(y-5)^2=4 and which has the least radius is

Nishant Vora IIT Patna
4 years ago
Condition of orhtogonality of 2 circles is

2 g g' + 2 f f' = c + c'

Apply this condition and keep in mind that radius of req circle should be least

Thanks
mycroft holmes
272 Points
4 years ago
Let the centres of the two circles be O1 and O2.

Any circle orthogonal to the two circles will have its centre on the radical axis and will pass through the limiting points of the co-axial system formed by the two given circles.

Its clear that among such circles, the one formed with the limiting points as the diameter will have the least radius. Hence we have to find the intersection of O1O2 and the radical axes. i.e. of the lines

5x = 7y and 14x+10y = 95 .