TS EAMCET · Maths · Parabola
If the angle between the tangents drawn to the parabola \(y^2=4 x\) from the points on the line \(4 x-y=0\) is \(\frac{\pi}{3}\), then the sum of the abscissae of all such points is
- A \(\frac{5}{3}\)
- B \(\frac{4}{7}\)
- C \(\frac{2}{5}\)
- D \(\frac{10}{13}\)
Answer & Solution
Correct Answer
(D) \(\frac{10}{13}\)
Step-by-step Solution
Detailed explanation
\(\tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{y_1^2 - 4(1)x_1}}{x_1+1}\) \(\sqrt{3} = \frac{\sqrt{(4x_1)^2 - 4x_1}}{x_1+1}\) \(3 = \frac{16x_1^2 - 4x_1}{(x_1+1)^2}\) \(3(x_1^2+2x_1+1) = 16x_1^2 - 4x_1\) \(3x_1^2+6x_1+3 = 16x_1^2 - 4x_1\) \(13x_1^2 - 10x_1 - 3 = 0\) Sum of…
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