First slide

Definition of a circle

Question

If the area of the circle
$4 x^{2} + 4 y^{2} - 8 x + 16 y + k = 0$ is $9 π$
square units, then the value of $k$ is

Moderate

A

4
B

16
C

-16
D

$\pm 16$

Solution

We have,
$4 x^{2} + 4 y^{2} - 8 x + 16 y + k = 0 \Rightarrow x^{2} + y^{2} - 2 x + 4 y + \frac{k}{4} = 0$
The radius of this circle is $\sqrt{1 + 4 - \frac{k}{4}} = \frac{\sqrt{20 - k}}{2}$
We have,
Area of the circle $= 9 π$ square units
$\Rightarrow π (\frac{20 - k}{4}) = 9 π \Rightarrow k = - 16$

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