The equation to the chord joining two points (x_1, y_1) and (x_2,… - Vidyadip

MCQ

The equation to the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is

✓
$\frac{x}{{{x_{1\,}}\, + \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, + \,\,{y_2}}}$ $ = 1$
B
$\frac{x}{{{x_{1\,}}\, - \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, - \,\,{y_2}}} = 1$
C
$\frac{x}{{{y_{1\,}}\, + \,\,{y_2}}}$+$\frac{y}{{{x_{1\,}}\, + \,\,{x_2}}} = 1$
D
$\frac{x}{{{y_{1\,}}\, - \,\,{y_2}}}$+$\frac{y}{{{x_{1\,}}\, - \,\,{x_2}}}= 1$

✓

Answer

Correct option: A.

$\frac{x}{{{x_{1\,}}\, + \,\,{x_2}}}$+$\frac{y}{{{y_{1\,}}\, + \,\,{y_2}}}$ $ = 1$

a
note that chord of $ xy = c^2$ whose middle point is $(h, k)$ in $\frac{x}{h}\, + \,\frac{y}{k}\, = \,2$ further, now $2h = x_1 + x_2 $ and $2k = y_1 + y_2$

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