JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A tangent and a normal are drawn at the point \(\mathrm{P}(2,-4)\) on the parabola \(\mathrm{y}^{2}=8 \mathrm{x}\), which meet the directrix of the parabola at the points \(\mathrm{A}\) and \(\mathrm{B}\) respectively. If \(Q(a, b)\) is a point such that \(A Q B P\) is a square, then \(2 \mathrm{a}+\mathrm{b}\) is equal to :
- A \(-16\)
- B \(-18\)
- C \(-12\)
- D \(-20\)
Answer & Solution
Correct Answer
(A) \(-16\)
Step-by-step Solution
Detailed explanation
Equation of tangent at \((2,-4)(\mathrm{T}=0)\) \(-4 y=4(x+2)\) \(x+y+2=0\ldots(1)\) equation of normal \(\mathrm{x}-\mathrm{y}+\lambda=0\) \(\downarrow(2,-4)\) \(\lambda=-6\) thus \(x-y=6 \ldots(2)\) equation of normal \(P O I\) of \((1) \,\&\, x=-2\) is \(A(-2,0)\)…
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