Thank you for registering.

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

Please check your email for login details.
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

A circle touches the lines y=x/√3 and y=√3x and has unit radius. Find its equation if center lies in first quadrant.

A circle touches the lines y=x/√3 and y=√3x and has unit radius. Find its equation if center lies in first quadrant. 

Grade:12th pass

1 Answers

kkbisht
90 Points
2 years ago
The two lines y= x/ \sqrt{}3 and y=\sqrt{}3 x are touching or tangenst to  the given unit circle having radius 1.Therefor using the condition that a line ax+by+c=0 is tangent to a circle  if the length of perpendicular from the centre to the line is equal to the radius(=1 ) in this case.
Let (h,k) be the  coordinates of  centre  in the first quadrant means h>0, k>0.
Now length of perpendicular from the centre to the line y= x/ \sqrt{}3  is = (k-h/\sqrt{}3)/\sqrt{}(1+1/3)=(k-h/\sqrt{}3)/\sqrt{}(4/3) =1
=>\sqrt{}3 k-h=2    -------(1)
 and similarly for other line the length of perpendicular from the centre to the line y= \sqrt{}3 x is (k-\sqrt{}3 h)/\sqrt{}4  =1
=>\sqrt{}3 h -k=2  –  ----(2)   
(1) =>h= 1+\sqrt{}3 and k=1+\sqrt{}3 .
Equation of Circle is:
(x-h)2 + ( y-k)2=1 => (x-1-\sqrt{}3)2  +(y-1-\sqrt{}3)2 =1
Now just simplify it. You get the required equation of the circle
kkbisht
 
 

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free