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Analytical Geometry

Hot goIITian

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11 Mar 2010 12:09:54 IST

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the lines L and K r symmetrc w.r.t the line Y=X IF THE EQUATION OF L IS Y=aX+b with a n b not =0 th

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the lines L and K r symmetrc w.r.t the line Y=XIF THE EQUATION OF L IS Y=aX+b with a n b not =0 then equation of K IS ........................................PLEASE ANSWER WITH STEPS

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TEJASWI V SHETTY.

Hot goIITian

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11 Mar 2010 12:43:26 IST

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is the ans X+AY=B?

TELL ME IF ITS RITE,DEN I'LL GIVE U D COMPLETE SOLN.

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Blazing goIITian

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11 Mar 2010 12:49:43 IST

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Let the equation of K be: y = mx + c

Therefore, any point on K is (h, mh + c)

Now, the mirror image of any (h, mh + c) wrt the line y = x lies on L(y = ax + b).

Apply the condition as stated above and get the values of 'm' and 'c'.

I hope you know how to find the mirror image of a point with respect to a line as a mirror.............

TEJASWI V SHETTY.

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11 Mar 2010 13:12:03 IST

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GOOD MY JOB IS REDUCED..THANKS.

THIS IS D METHOD FRM WHCH I GOT D ANS.

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Blazing goIITian

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11 Mar 2010 13:17:59 IST

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AN ALTERNATE APPROACH ( FOR IIT-JEE)

Consider the case given below:

As can be seen, the intercepts of the two symmetric lines are exchanged i.e. x-intrcpt of L = y-intrcpt of K and vice versa.............

So, convert the equation of L into intercept form and then exchange the values of x and y intercepts. U'll arrive at the equation for K.

Yagyadutt Mishra

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11 Mar 2010 14:14:27 IST

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Property : Reflection of any point (a,b) in the line y=x is (b,a)

Now L and K are symmtrical.....

So if (a1,b1) and (a2,b2) are two points on the Line L....then correspondigly (b1,a1) and (b2,a2) will be the points on the Line K

Now we have given L : y = ax+b

put x=0 y = b points is (0,b)

put x=1 y= (a+b) points is (1,a+b)

So line K will have points (b,0) and (a+b,1) on it....

SO equation is (y-0) = (1)/a ( x -b)

So ay = x -b is the equation of K

THE GREAT

Hot goIITian

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13 Mar 2010 07:47:43 IST

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thanks for all the answer is right

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