Min { ( x 1 − x 2 ) 2 + ( 12 + 1 − x 1 2 − 4 x 2 ) 2 } ∀ x 1 , x 2 ∈ R is

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Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangents & NormalsHard2 minQB

MathematicsHardsingle choice

$Min {(x_{1} - x_{2})^{2} + (12 + 1 - x_{1}^{2} - 4 x_{2})^{2}} \forall x_{1}, x_{2} \in R$ is

Options:

Answer:

Solution:

Let $y_{1} = 12 + 1 - x_{1}^{2}$ and $y_{2} = 4 x_{2}$ $(y_{1} - 12)^{2} = 1 - x_{1}^{2} \Rightarrow x_{1}^{2} + (y_{1} - 12)^{2} = 1; y_{2}^{2} = 4 x_{2}$

Required answer is shortest distance between two curves $x^{2} + (y - 12)^{2} = 1$ and $y^{2} = 4 x$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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