AP EAMCET · Maths · Straight Lines
When the coordinate axes are rotated through an angle of \(45^{\circ}\) about the origin in the positive direction, if the transformed equation of a curve is \(17 x^2-16 x y+17 y^2=225\), then the original equation of that curve is
- A \(25 x^2+9 y^2=225\)
- B \(9 x^2-25 y^2=225\)
- C \(25 x^2-16 x y+9 y^2=225\)
- D \(9 x^2+25 y^2=225\)
Answer & Solution
Correct Answer
(A) \(25 x^2+9 y^2=225\)
Step-by-step Solution
Detailed explanation
When the axes are rotated through \(45^{\circ}\) about the origin in the positive direction then replace \((x, y)\) by \(\left(\frac{x}{\sqrt{2}}+\frac{y}{\sqrt{2}}, \frac{-x}{\sqrt{2}}+\frac{y}{\sqrt{2}}\right)\) So, original equation of the curve,…
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