AP EAMCET · Maths · Parabola
The locus of the point of intersection of the normals to the parabola \(x^2=8 y\), which are at right angles to each other, is
- A \(y^2=2 x-5\)
- B \(y^2=x-12\)
- C \(x^2=y-10\)
- D \(x^2=2 y-12\)
Answer & Solution
Correct Answer
(D) \(x^2=2 y-12\)
Step-by-step Solution
Detailed explanation
\(x^2 = 8y \Rightarrow 4a = 8 \Rightarrow a=2\) The equation of a normal to \(x^2=4ay\) with slope \(m\) is \(m^3x - m^2y + 2am^2 + a = 0\). Let \((x,y)\) be the intersection point. If \(m_1, m_2, m_3\) are the slopes, and \(m_1 m_2 = -1\).…
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