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

Question

Dr. Abubacker · Accepted Answer

(d)
Any point on the line $x - y - 5 = 0$ will be of the form $(t,\ t - 5)$ Chord of contact of this point with respect to curve $x^{2} + {4y}^{2} = 4$ is
$tx + 4(t - 5)y - 4 = 0$
$\Rightarrow ( - 20y - 4) + t(x + 4y) = 0$
Which is a family of straight lines, each member of this family pass through point of intersection of straight lines $- 20y - 4 = 0$ and $x + 4y = 0$ which is $\left( \frac{4}{5}, - \frac{1}{5} \right)$

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

Explanation

Reviewed by Dr. Abubacker

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