Find the equation of the straight lines joining the origin to the points of intersection of the line $3 x + 4 y - 5 = 0$ and the curve $2 x^{2} + 3 y^{2} = 5$ .

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Solution

We have,
$\begin{matrix} \frac{3 x + 4 y}{5} = 1 2 x^{2} + 3 y^{2} = 5 \frac{{(3 x + 4 y)}^{2}}{{(5)}^{2}} 2 x^{2} + 3 y^{2} = \frac{9 x^{2} + 16 y^{2} + 24 x y}{5} 10 x^{2} + 15 y^{2} = 9 x^{2} + 16 y^{2} + 24 x y x^{2} = y^{2} + 24 x y x^{2} - y^{2} - 24 x y = 0 \end{matrix}$

Equation of line joining origin and prove that of intersection of line $3 x + 4 y = 5$ & Curve $2 x^{2} + 3 y^{2} = 5$ .

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Find the equation of the straight lines joining the origin to the points of intersection of the line 3x+4y−5=0 and the curve 2x2+3y2=5.

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