1057@vivek....u gave a general equation of a line.....has to be in that form....but u hav to specify the values of a',b',c' in terms of a,b and c....
given a line with its equation ax + by + c = 0
suppose we rotate the co-ordinate axis with an angle of 78°,
what will happen to the eqn. of the line?
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11 Answers
105721Representing line as xcosθ+ysinθ=p
We get θ=tan-1(b/a) and p=-c/√a2+b2
Rotating co-ordine axes corresponds to rotating line about origin.
Now p remains same while θ=θ+78.
New equation,
xcos(78+tan-1(b/a))+ysin(78+tan-1(b/a))=-c/√a2+b2 (ans)
36well sorry for the horrible title ....
"Thinks and answer"....
rather would be
"Think and answer"...... :P
36yea...
well rather useful question would be..
A line has intercepts 'a' and 'b' on the co-ordinate axis. The axis is then rotated with an angle keeping the origin fixed. The line now makes the intercepts 'p' and 'q' on this rotated axis. What relation can you find between 'a' , 'b' , 'p' and 'q' ???
36question from JEE..........
Answer wasn't needed......... Answer + soln. was required
262eqn of original line - xa +yb = 1
eqn of new line - xp + yq = 1
now since on rotation the perp. distance from origin remains same ,
|0+0-1|√1/a2 + 1/b2 = |0+0-1|√1/p2 + 1/q2
hence 1a2 + 1b2 = 1p2 + 1q2
1that is the exact same solution given in the official jee solution.