Q) The set of values of "a" for which circle with center (0,1) & radius is 1, meet the parabola y equals a x squared at a point other than origin is left parenthesis A right parenthesis a greater than 0 space space space left parenthesis B right parenthesis a element of open parentheses 0 comma 1 half close parentheses space space left parenthesis C right parenthesis space a element of space open parentheses 1 fourth comma 1 half close parentheses space space space left parenthesis D right parenthesis space a element of open parentheses 1 half comma infinity close parentheses

Asked by araima2001 | 31st Mar, 2017, 05:24: AM

Expert Answer:

begin mathsize 16px style Given space that space straight a space circle space with space centre space left parenthesis 0 comma 1 right parenthesis space and space radius space is space 1 space then space equation space of space the space circle
straight x squared plus open parentheses straight y minus 1 close parentheses squared equals 1
straight x squared plus straight y squared minus 2 straight y plus 1 equals 1
straight x squared plus straight y squared minus 2 straight y equals 0 space space space....... left parenthesis straight i right parenthesis
also comma
straight y equals ax squared space..... left parenthesis ii right parenthesis
after space solving space these space equations space simultaneously space we space get comma
left parenthesis straight x comma straight y right parenthesis equals open parentheses fraction numerator square root of 2 straight a minus 1 end root over denominator straight a end fraction comma fraction numerator 2 straight a minus 1 over denominator straight a end fraction close parentheses
As space 2 straight a minus 1 space can space not space be space less than 0
we space have space 2 straight a minus 1 greater than 0
rightwards double arrow straight a greater than 1 half
The space answer space is space open parentheses 1 half comma infinity close parentheses.
end style

Answered by Sneha shidid | 31st Mar, 2017, 03:10: PM