Given that the equation of the circle is ${{x}^{2}}+{{y}^{2}}-4x+2y+k=0$ where $k$ is a con

Question

Given that the equation of the circle is ${{x}^{2}}+{{y}^{2}}-4x+2y+k=0$ where $k$ is a constant. Determine the value of $k$ for each of the following cases: The area of the circle is $9\pi $ square units. Also, state the centre of this circle. The line $y=x$ is a tangent to the circle.

Accepted Answer

$\text{(a) }k=-4,\ \text{centre }(2,-1)$ $\text{(b) }k=\dfrac{1}{2}$

Finding an unknown in the circle equation

Finding an unknown in the circle equation

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