AP EAMCET · Maths · Parabola
If \(x-y-3=0\) is a normal drawn through the point \((5,2)\) to the parabola \(y^2=4 x\), then the slope of the other normal that can be drawn through the same point to the parabola \(y^2=4 x\) is
- A \(0\)
- B \(-1\)
- C \(2\)
- D \(-2\)
Answer & Solution
Correct Answer
(D) \(-2\)
Step-by-step Solution
Detailed explanation
Equation of normal to \(y^2=4ax\) is \(y = mx - 2am - am^3\). For \(y^2=4x\), \(a=1\). So, \(y = mx - 2m - m^3\). Normal passes through \((5,2)\): \(2 = 5m - 2m - m^3 \Rightarrow m^3 - 3m + 2 = 0\). Given normal \(x-y-3=0 \Rightarrow y=x-3\). Slope \(m_1=1\). Factor the cubic…
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