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AP EAMCET · Maths · Circle

If the equation of a curve C is transformed to 9x2+25y2=225 by the rotation of the coordinate axes about the origin through an angle π4 in the positive direction then the equation of the curve C, before the transformation is

  1. A 17x2+16xy+17y2=225
  2. B 17x2+23y2=391
  3. C 17x2-16xy+17y2=225
  4. D 23x2+17y2=391
Verified Solution

Answer & Solution

Correct Answer

(C) 17x2-16xy+17y2=225

Step-by-step Solution

Detailed explanation

The original and new coordinates are, x=xcosπ4-ysinπ4=x2-y2 y=xsinπ4+ycosπ4=x2+y2 The equation of the curve is, 9x2+25y2=225 ⇒x-y22+25x+y22=225 After simplification, 9x2+9y2+18xy+25x2+25y2-50xy=450 ⇒34x2+34y2-32xy=450 ⇒17x2+17y2-16xy=225