First slide

Pair of straight lines

Question

The equation to the pair of lines joining the origin to the points of intersection of y = x+3 and $2 x^{2} + 2 y^{2} = 1$ is

Moderate

A

$12 (x^{2} + y^{2}) = {(x - y)}^{2}$
B

$6 (x^{2} + y^{2}) = {(x - y)}^{2}$
C

$18 (x^{2} + y^{2}) = {(x - y)}^{2}$
D

$2 (x^{2} + y^{2}) = {(x - y)}^{2}$

Solution

$\frac{x - y}{- 3} = 1 \Rightarrow a p p l y h o m o g e n i z a t i o n$
$2 x^{2} + 2 y^{2} = {(\frac{y - x}{3})}^{2}$
$18 (x^{2} + y^{2}) = {(x - y)}^{2}$

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