AP EAMCET · Maths · Straight Lines
If the equation \(3 x^2+4 y^2-x y+k=0\) is the transformed equation of \(3 x^2+4 y^2-x y-5 x-7 y+2=0\) after shifting the origin to the point \((\alpha, \beta)\) by the translation of axes, then \(\alpha+\beta-\mathrm{k}=\)
- A -2
- B 6
- C 3
- D -1
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
\(6\alpha - \beta - 5 = 0\) \(-\alpha + 8\beta - 7 = 0\) \(\alpha = 1, \beta = 1\) \(k = 3(1)^2 + 4(1)^2 - (1)(1) - 5(1) - 7(1) + 2\) \(k = 3 + 4 - 1 - 5 - 7 + 2 = -4\) \(\alpha + \beta - k = 1 + 1 - (-4) = 6\)
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