First slide

Definition of a circle

Question

If the tangents are drawn from any point on the line x +y= 3 to the circle $x^{2} + y^{2} = 9$ ,then the chord of contact passes through the Point

Moderate

A

(3, 5)
B

(3, 3)
C

(5, 3)
D

none of these

Solution

Let $(α, 3 - α)$ be any point on ,x+y=3.
Then, the equation of chord of contact is
$\begin{aligned} αx + (3 - α) y = 9 \\ α (x - y) + 3 y - 9 = 0 \end{aligned}$
Therefore, the chord passes though the point (3, 3) for all values of $α$ .

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