The equation $x^2+y^2+6x-4y=k$, where $k$ is a constant, represents a circle. State the con

Question

The equation $x^2+y^2+6x-4y=k$, where $k$ is a constant, represents a circle. State the condition on $k$ for the radius to be positive.[1] Find the value of $k$ for which $y=2x+1$ is tangent to the circle.[3] Find the ranges of $k$ for which the line meets the circle at two distinct points, and for which it does not meet the circle.[2]

Accepted Answer

(a) $k>-13$. (b) $k=-\dfrac{16}{5}$. (c) Two points: $k>-\dfrac{16}{5}$; no intersection: $-13

When a line meets a circle

When a line meets a circle

Solution:

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