Mathematics Class 10 Lab Manual | 21 Lab Activities

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RESOURCE CENTRE
Lab Activities
Mathematics
10+1
Activity-3

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Solution:
The equation of the given circle is

$$x^2 + y^2 + 8x - 16y + 64 = 0$$
$$\Rightarrow x^2 + 8x + 16 + (y^2 - 16y + 64) = 16$$
$$\Rightarrow (x + 4)^2 + (y - 8)^2 = 4^2$$
$$\Rightarrow \{ x - (-4) \}^2 + (y - 8)^2 = 4^2$$

Clearly, the center of the circle is $(-4, 8)$ and its radius is 4.

The image of the center after reflection in the line $x = 0$ is $(4, 8)$.

So, the equation of the reflected circle is

$$(x - 4)^2 + (y - 8)^2 = 4^2$$

Expanding the equation:

$$x^2 - 8x + y^2 - 16y + 64 = 0$$

Thus, the equation of the reflected circle is

$$x^2 - 8x + y^2 - 16y + 64 = 0$$