Circle 5 Question 9
9. The chords of contact of the pair of tangents drawn from each point on the line $2 x+y=4$ to the circle $x^{2}+y^{2}=1$ pass through the point… .
(1997, 2M)
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Answer:
Correct Answer: 9. $\frac{1}{2}, \frac{1}{4}$
Solution:
- A point on the line $2 x+y=4$ is of the form $(h, 4-2 h)$.
Equation of the chord of contact is $T=0$ i.e.
$$ h x+(4-2 h) y=1 \Rightarrow(4 y-1)+h(x-2 y)=0 $$
This line passes through the point of intersection of $4 y-1=0$ and $x-2 y=0$ i.e. through the point $\frac{1}{2}, \frac{1}{4}$.
