AP EAMCET · Maths · Parabola
If a focal chord of the parabola \(y^2=4 x\) makes an angle \(45^{\circ}\) with positive \(\mathrm{X}\)-axis, then the slopes of the normals drawn at the ends of the focal chord will satisfy the equation
- A \(x^2-2 x-1=0\)
- B \(x^2+2 x-1=0\)
- C \(x^2-1=0\)
- D \(x^2+2 x-2=0\)
Answer & Solution
Correct Answer
(B) \(x^2+2 x-1=0\)
Step-by-step Solution
Detailed explanation
\(a=1\) \(t_1 t_2 = -1\) \(\frac{2a(t_2-t_1)}{a(t_2^2-t_1^2)} = \tan 45^{\circ}\) \(\frac{2}{t_1+t_2} = 1 \implies t_1+t_2 = 2\) \(m_1 = -t_1, m_2 = -t_2\) \(m_1+m_2 = -(t_1+t_2) = -2\) \(m_1 m_2 = (-t_1)(-t_2) = t_1 t_2 = -1\) \(x^2 - (m_1+m_2)x + m_1m_2 = 0\)…
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