TS EAMCET · Maths · Parabola
If two distinct chords drawn from the point \(A(4,4)\) on the parabola \(y^2=4 x\) are bisected by the line \(y=a x\), then the interval in which \(a\) lies is
- A \(\left(\frac{1}{2}-\frac{1}{\sqrt{2}}, \frac{1}{2}+\frac{1}{\sqrt{2}}\right)\)
- B \(\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)\)
- C \(\left(\frac{1+\sqrt{2}}{2}, \frac{5+\sqrt{2}}{2}\right)\)
- D \((2, \infty)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{1}{2}-\frac{1}{\sqrt{2}}, \frac{1}{2}+\frac{1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Let the point of intersection of the line \(y=a x\) with the chord be \((\alpha, a 0)\), then \(\alpha=\frac{4+x_1}{2}\) \( \Rightarrow x_1=2 \alpha-4 \text { and } a \alpha=\frac{4+y_1}{2} \Rightarrow y_1=2 a \alpha-4 \) As \(\left(x_I, y_1\right)\) lies on the parabola…
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