TS EAMCET · Maths · Parabola
If \(\mathrm{m}_1\) and \(\mathrm{m}_2\) are the slopes of the tangents drawn from the point \((1,4)\) to the parabola \(y^2=11 x\) then \(2\left(\mathrm{~m}_1{ }^2+\mathrm{m}_2{ }^2\right)=\)
- A 24
- B 22
- C 21
- D 18
Answer & Solution
Correct Answer
(C) 21
Step-by-step Solution
Detailed explanation
Equation of tangent: \(y = mx + \frac{11}{4m}\) Substitute \((1,4)\): \(4 = m + \frac{11}{4m}\) \(4m^2 - 16m + 11 = 0\) \(m_1+m_2 = -\frac{-16}{4} = 4\) \(m_1m_2 = \frac{11}{4}\) \(2(m_1^2+m_2^2) = 2((m_1+m_2)^2 - 2m_1m_2)\) \(= 2((4)^2 - 2(\frac{11}{4}))\)…
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