TS EAMCET · Maths · Parabola
The angle between the tangents drawn from the point \((1,4)\) to the parabola \(y^2=4 x\) is
- A \(\frac{\pi}{3}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{3 \pi}{4}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{3}\)
Step-by-step Solution
Detailed explanation
Given, \(y^2=4 x\) \[ [\therefore a=1] \] General equation of parabola \(=y=m x+\frac{a}{m}\) [where, \(m\) is the slope] at \((1,4) ; 4=m+\frac{a}{m}\) \[ \Rightarrow 4=m+\frac{1}{m} \Rightarrow m^2-4 m+1=0 \] Let \(m_1\) and \(m_2\) are the roots.…
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