The combined equation of straight lines joining the origin to the points of intersection the line y=2x+1 with the curve $x^{2} + y^{2} + 2 x y + 4 = 0$ is given by

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Solution

The correct option is C

The equation of straight lines in the method of homogenization is given by

$x^{2} + y^{2} + 2 x y + 4 {(\frac{y - 2 x}{1})}^{2} = 0$

[we are making each term second degree by multiplying by the appropriate powers of $(\frac{y - 2 x}{1})$ ]

$\Rightarrow x^{2} + y^{2} + 2 x y + 4 (y^{2} + 4 x^{2} - 4 x y) = 0$

$\Rightarrow 17 x^{2} + 5 y^{2} - 14 x y = 0$

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The combined equation of straight lines joining the origin to the points of intersection the line y=2x+1 with the curve x2+y2+2xy+4=0 is given by

The correct option is C The equation of straight lines in the method of homogenization is given by x2+y2+2xy+4(y−2x1)2=0 [we are making each term second degree by multiplying by the appropriate powers of (y−2x1)] ⇒x2+y2+2xy+4(y2+4x2−4xy)=0 ⇒17x2+5y2−14xy=0

The combined equation of straight lines joining the origin to the points of intersection the line y=2x+1 with the curve $x^{2} + y^{2} + 2 x y + 4 = 0$ is given by