First slide

Pair of straight lines

Question

The image of the pair of lines represented by $a x^{2} + 2 h x y + b y^{2} = 0 by the line mirror y = 0 is$

Easy

A

$a x^{2} - 2 h x y - b y^{2} = 0$
B

$b x^{2} - 2 h x y + a y^{2} = 0$
C

$b x^{2} + 2 h x y + a y^{2} = 0$
D

$a x^{2} - 2 h x y + b y^{2} = 0$

Solution

Each point (x, y) has an image in line y = 0 as (x, -y).
So, replacing y by - y in the given equation, we get the image $as a x^{2} - 2 h x y + b y^{2} = 0$

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