Tangents are drawn from the point on the line $x - y - 5 = 0$ to ${x^2} + 4{y^2} = 4$, then all the chords of contact pass through a fixed point, whose coordinates are

$\left( {\frac{1}{5},\;\frac{4}{5}} \right)$

JEE MATHEMATICS MCQ: ELLIPSE

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Application +4 | -1

Tangents are drawn from the point on the line

x - y - 5 = 0

{x^2} + 4{y^2} = 4

, then all the chords of contact pass through a fixed point, whose coordinates are

View answer and explanation

Correct option: D

\left( {\frac{4}{5},\; - \frac{1}{5}} \right)

Option D (

\left( {\frac{4}{5},\; - \frac{1}{5}} \right)

) is correct because the chord of contact passes through a fixed point which is the intersection of two lines derived from the equation of the chord of contact.

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(\sqrt{7}, 0)

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P

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9 x^{2}+16 y^{2}=144

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\mathrm{PA}+\mathrm{PB}

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O

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