(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

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(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 $xy = 0$.

Class 11 Mathematics Pair of straight lines Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

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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

A
$(x + y)^2 = 9$
B
$x^2 + (3 - x)^2 = 9$
C
$xy = 0$
D
$(3 - x)^2 + y^2 = 9$

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Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

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