Question56 If $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in harmonic progression (HP). and the straight-line $a x+2 b y+c=0$ passes through the points $(2, k)$ and $(-1,3)$, find the value of $k$

Studdy Solution
From Equation 5, solve for $a$:
$$-2a + 8b = 0$$
$$2a = 8b$$
$$a = 4b$$
Substitute $a = 4b$ into Equation 4:
$$4b + 2bk + 2b = 0$$
$$6b + 2bk = 0$$
$$2b(3 + k) = 0$$
Since $b \neq 0$, we have:
$$3 + k = 0$$
$$k = -3$$
The value of $k$ is:
$$\boxed{-3}$$