IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

maddy12345

Transform the above equation -----------

14x² -4xy+11y²-36x+ 48y+ 41y = 0 in the form ax²+by² = 1 by suitable change of axis.

Solve this puzzle buddy. Good luck.

venkat_tatolu

write x=X+h and y=Y+k in the given equation .Where (h,k) is the new origin.

Now make the coefficients of X and Y as zero.Because in the answer there are no first degree terms.

nadeemoidu

u shd rotate the axis not change the origin.

nadeemoidu

Is it ( 4/369) X² + (11/369) Y² = 1 ?

kane

use the formula X=x cos theta - y sin theta and Y= x sin theta + y cos theta.then after simplifying the equation after putting the values of the above X and Y in the given equation,check the coefficient of x and y.both of them are equal to zero.solve the 2 equations to get the value of theta.rate me if useful.

plzzzzzzzzz

nadeemoidu

That was not exactly my approach.

1) use the formula X=x cos theta - y sin theta and Y= x sin theta + y cos theta.
( Here u rotate the axes).

2)after simplifying the equation after putting the values of the above X and Y in the given equation,check the coefficient of xy , since it is not there in the final equation , equate it to 0 . Thus u'll get theta.

3) now substitute theta in the equation.

4) now remove the coefficients of x and y ( not x2 and y2 ) . use X= x+h, Y=y+k and the method of completing the squares.

Here u r changing the origin. Now u get the answer.

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