Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
let chord of circle is AB ...drop a perpendicular on this chord it will bisect the chord , let this point be C ...
then AC = BC = 1/2
let O be the center of circle then in triangle AOC ...
AO = radius of circle , AC = 1/2
OC = d ( this can be calculated by eq of line)
perpendicular distance from (0,0) to line x+y=k will be K/root2 ...
now using pythogorus theorem
AO2 = AC2 + OC2
1 = 1/4 + k2/2
k2 = 3/2
k = + or - 3/2 so
there are 2 possible values for k
ploting the approx graph we see that the unit circle is bieng cut by the line for diff values of k
now for k=0 the line is y=-x and its chord length is the diammeter ie 2
not moving up as we increase k to 1 we get a line through the end points of the circle ie (0,1)and(-1,0) and now the distance is
2^1/2 units which is greater than 1
clearly as we move from k=0 to k=1 the chord length is gradually decreasing
and now we still increase k
and by logic we can see that the chord length decrease and it will reach 1 for some value
as the whole thing and our arguements are symmetrical about the x axis ie for k negaive
so there are two values when this happens
so the answer is 2
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !