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Question

(C) Given equations are $x^2 + y^2 = 9$ $(i)$ and $x + y = 3$ $(ii)$.To find the equation of the pair of lines joining the origin to the intersection

Vedclass · Accepted Answer

$xy = 0$

Vedclass · Answer

(C) Given equations are $x^2 + y^2 = 9$ $(i)$ and $x + y = 3$ $(ii)$.To find the equation of the pair of lines joining the origin to the intersection points,we homogenize equation $(i)$ using equation $(ii)$.From $(ii)$,we have $\frac{x + y}{3} = 1$.Substituting this into $(i)$,we get $x^2 + y^2 = 9 \left( \frac{x + y}{3} \right)^2$.$x^2 + y^2 = 9 \left( \frac{x^2 + y^2 + 2xy}{9} \right)$.$x^2 + y^2 = x^2 + y^2 + 2xy$.$2xy = 0 \Rightarrow xy = 0$.Thus,the required equation is $xy = 0$.

The equation of the pair of lines joining the origin to the points of intersection of $x^2 + y^2 = 9$ and $x + y = 3$ is

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