WBJEE · Maths · Parabola
If \(y=4 x+3\) is parallel to a tangent to the parabola \(y^{2}=12 x\), then its distance from the normal parallel to the given line is
- A \(\frac{213}{\sqrt{17}}\)
- B \(\frac{219}{\sqrt{17}}\)
- C \(\frac{211}{\sqrt{17}}\)
- D \(\frac{210}{\sqrt{17}}\)
Answer & Solution
Correct Answer
(B) \(\frac{219}{\sqrt{17}}\)
Step-by-step Solution
Detailed explanation
Given equation of parabola is \[ y^{2}=12 x \] On differentiating both sides w.r.t. \(x,\) we get \[ 2 y \frac{d y}{d x}=12 \Rightarrow \frac{d y}{d x}=\frac{6}{y} \] Since, the normal to the curve is parallel to the line \(y=4 x+3\) \(\therefore\) Slope of normal curve \(=\)…
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