First slide

Equation of line in Straight lines

Question

Locus of the mid-points of the intercepts between the coordinate axes by the lines passing through $(a, 0)$ does not intersect

Moderate

A

$x - a x i s$
B

$y - a x i s$
C

$y = x$
D

$y = a$

Solution

Equation of any line through $(a, 0)$ be $\frac{x}{a} + \frac{y}{b} = 1$ where $b$ is a parameter. This line meets $y - a x i s$ t $(0, b)$ and if $(h, k)$ denotes the mid-point of the intercept of the line between the coordinate axes, then $h = a / 2, k =$ $b / 2$ and then the locus of $(h, k) is x = a / 2$ . This clearly does not intersect $y - a x i s$ .

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