TS EAMCET · Maths · Straight Lines
The equation of a curve \(C\) is transformed to \(X^2+Y^2-6 X+8 Y+21=0\) by the rotation of coordinate axes about the origin through an angle of \(\frac{\pi}{4}\) in the positive direction of \(X\)-axis. If \(a x^2+b y^2+c x+d y+e=0\) is the equation of the curve \(C\) before the transformation, then \(\left(a+b+c^2+d^2-5 e\right)^2=0\).
- A 4
- B 9
- C 16
- D 25
Answer & Solution
Correct Answer
(B) 9
Step-by-step Solution
Detailed explanation
Given, transformed equation is \(x^2+y^2-6 x+8 y+21=0\) Now, \(\begin{aligned} & X^{\prime}=x \cos \pi / 4-Y \sin \pi / 4=\frac{X-Y}{\sqrt{2}} \\ & Y^{\prime}=x \sin \pi / 4+Y \cos \pi / 4=\frac{X+Y}{2} \end{aligned}\) Before transformation, the equation is…
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