First slide

Definition of a circle

Question

If a chord of a circle $x^{2} + y^{2} = 25$ with one
extremity at $(4, 3)$ subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be

Moderate

A

$(- 3, - 4)$
B

$(4, - 3)$
C

$(3, 4)$
D

$(- 3, 4)$

Solution

Let P be the point $(4, 3)$ and $Q (h, k)$ be the other extremity of the chord through $P$ . Centre of the circle is the origin $0$ . Then $O P$ is perpendicular to $O Q$
$\Rightarrow \frac{k}{h} \times \frac{3}{4} = - 1 \Rightarrow \frac{k}{h} = - \frac{4}{3}$
which is satisfied by $(h, k) = (- 3, 4)$

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