AP EAMCET · Maths · Ellipse
If the lines \(2 x-y+3=0\) and \(4 x+k y+3=0\) are conjugate with respect to the ellipse \(5 x^2+6 y^2-15=0\), then \(k\) equals
- A \(1\)
- B \(2\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(2 x-y+3=0\) and \(4 x+k y+3=0\) are conjugate with respect to ellipse \(5 x^2+6 y^2-15=0\) We know that \(a_1 x+b_1 y+c_1=0\) and \(a_2 x+b_2 y+c_2=0\) are conjugate with \(\frac{x^2}{a^2}+\frac{y^2}{b}=1\) Then, \(a^2 a_1 a_2+b^2 b_1 b_2=c_1 c_2\) \(\therefore\) Here,…
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