AP EAMCET · Maths · Parabola
If the axes are rotated through an angle \(45^{\circ}\) about the origin in anticlockwise direction, then the transformed equation of \(y^2=4 a x\) is
- A \((x+y)^2=4 \sqrt{2} a(x-y)\)
- B \((x-y)^2=4 \sqrt{2} a(x+y)\)
- C \((x-y)^2=\frac{4 a}{\sqrt{2}}(x+y)\)
- D \((x+y)^2=\frac{4 a}{\sqrt{2}}(x-y)\)
Answer & Solution
Correct Answer
(A) \((x+y)^2=4 \sqrt{2} a(x-y)\)
Step-by-step Solution
Detailed explanation
Given \(\theta=45^{\circ}\) Let new co-ordinate be \(\left(x^{\prime}, y^{\prime}\right)\) and old coordinate be \((x, y)\) So, \(x=x^{\prime} \cos 45^{\circ}-y^{\prime} \sin 45^{\circ}=\frac{x^{\prime}-y^{\prime}}{\sqrt{2}}\) and…
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