When the coordinate axes are rotated about the origin in the positive direction through an angle 4, if the equation 49x^2+25y^2=1225 is transformed to px^2+ qxy+ry^2=t and the G.C.D of p ,q ,r ,t is…

Question

When the coordinate axes are rotated about the origin in the positive direction through an angle 4, if the equation 49x^2+25y^2=1225 is transformed to px^2+ qxy+ry^2=t and the G.C.D of p ,q ,r ,t is 1 , then

Accepted Answer

Correct answer: C. (c) We have an equation 49x^2+25y^2=1225…………..(i) Since coordinate axes are rotated through an angle 4 (positive direction) ⇒x= x^ ' 2- y^ ' 2…………….(ii) and y= x^ ' 2+ y^ ' 2……………..(iii) Putting values from (ii) and (iii) into the equation (i) 49( x^ ' 2- y^ ' 2)^2+25( x^ ' 2+ y^ ' 2)^2=1225 ⇒37x^ '2-24x^ 'y^ '+37y^ '2=1225 Here , p=37 ,q=-24 ,r=37 ,t=1225 ⇒ (p+q+r-15 )^2=t=1225

$When the coordinate axes are rotated about the origin in the positive direction through an angle \frac{π}{4}, if the equation 49 x^{2} + 25 y^{2} = 1225 is transformed to p x^{2} + qxy + r y^{2} = t and the G.C.D of p, q, r, t is 1 , then$

Solution

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