Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

Minimum distance between $y^{2} - 4 x - 8 y + 40 = 0$ and $x^{2} - 8 x - 4 y + 40 = 0$

Answer:

Solution:

since two parabolas are symmetrical about $y = x$ .

Solving $y = x & y^{2} - 4 x - 8 y + 40 = 0$

$\Rightarrow x^{2} - 12 x + 40 = 0$

has no real solution

∴ They don't intersect

Point on $(x - 4)^{2} = 4 (y - 6)$ is $(6, 7)$ and the corresponding point on $(y - 4)^{2} = 4 (x - 6)$ is $(7, 6)$ minimum distance is $2$ .

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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