AP EAMCET · Maths · Ellipse
The value of ' \(k\) ' so that the line \(y=2 x+k\) may touch the ellipse \(3 x^2+5 y^2=15\) is
- A \(\pm \sqrt{23}\)
- B \(\pm \sqrt{13}\)
- C \(\pm \sqrt{33}\)
- D \(\pm \sqrt{32}\)
Answer & Solution
Correct Answer
(A) \(\pm \sqrt{23}\)
Step-by-step Solution
Detailed explanation
For \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) and \(y=m x+c\) is tangent Condition of tangency is \(\left(c^2=a^2 m^2+b^2\right)\) Here, \(\frac{x^2}{5}+\frac{y^2}{3}=1\) and \(y=2 x+k\) is a tangent…
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