TS EAMCET · Maths · Pair of Lines
By rotating the axes through an angle of \(30^{\circ}\) in the anti-clockwise direction about the origin, the equation \(4 x^2+12 x y+9 y^2+6 x+9 y+2=0\) becomes \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) then
- A \(\quad a=21-6 \sqrt{3}\)
- B \(g / f=\frac{3+2 \sqrt{3}}{3 \sqrt{3}-2}\)
- C \(b=31+6 \sqrt{3}\)
- D \(c=6\)
Answer & Solution
Correct Answer
(B) \(g / f=\frac{3+2 \sqrt{3}}{3 \sqrt{3}-2}\)
Step-by-step Solution
Detailed explanation
\(\therefore\) We are given that axis rotated through an angle of \(30^{\circ}\). Now let new co-ordinates of the curve is \((\mathrm{X}, \mathrm{Y})\) Now \(\mathrm{X}=x \cos \alpha-\mathrm{y} \sin \alpha, \mathrm{Y}=\mathrm{x} \sin \alpha+\mathrm{y} \cos \alpha\)…
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