JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(P ( h , k )\) be point on the parabola \(x =4 y ^2\), which is nearest to the point \(Q(0,33)\), then the distance of \(P\) from the directrix of the parabola \(y ^2=4( x + y )\) is equal to :
- A \(2\)
- B \(4\)
- C \(8\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
Equation of normal \(y=-t x+2 a t+a t^3\) \(y=-t x+\frac{2}{16} t+\frac{1}{16} t^3\) It passes through \((0,33)\) \(33=\frac{ t }{8}+\frac{ t ^3}{16}\) \(t ^3+2 t -528=0\) \(( t -8)\left( t ^2+8 t +66\right)=0\) \(t =8\)…
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