First slide

Definition of a circle

Question

The point diametrically opposite to the point
$P (1, 0)$ on the circle $x^{2} + y^{2} + 2 x + 4 y - 3 = 0,$ is

Moderate

A

(-3,-4)
B

(3, 4)
C

(3, -4)
D

(-3, 4)

Solution

The coordinate of the centre of the circle are
$(- 1, - 2) .$ Let Q $(a, b)$ be diametrically opposite to $P .$ Then,
mid-point of $P Q$ is the centre of the circle.
$∴ \frac{a + 1}{2} = - 1$ and $\frac{b + 0}{2} = - 2 \Rightarrow a = - 3$ and $b = - 4$
Hence, required point is (- 3, - 4).

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