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Number of intersecting points of the conics $4 x^{2}+9 y^{2}=1$ and $4 x^{2}+y^{2}=4$ is
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For curve I.
$4 x^{2}+9 y^{2}=1 \Rightarrow \frac{x^{2}}{\left(\frac{1}{2}\right)^{2}}+\frac{y^{2}}{\left(\frac{1}{3}\right)^{2}}=1$
which is an equation of ellipee with $a=\frac{1}{2}$ and $b=\frac{1}{3}$
For curve $I I, 4 x^{2}+y^{2}=4$ $\Rightarrow \quad \frac{x^{2}}{1}+\frac{y^{2}}{4}=1$
$\Rightarrow \quad \frac{x^{2}}{(1)^{2}}+\frac{y^{2}}{(2)^{2}}=1$
which is also an equation of ellipse with $a=1$ and $b=2$
Hence, there is no intersecting point.
$4 x^{2}+9 y^{2}=1 \Rightarrow \frac{x^{2}}{\left(\frac{1}{2}\right)^{2}}+\frac{y^{2}}{\left(\frac{1}{3}\right)^{2}}=1$
which is an equation of ellipee with $a=\frac{1}{2}$ and $b=\frac{1}{3}$
For curve $I I, 4 x^{2}+y^{2}=4$ $\Rightarrow \quad \frac{x^{2}}{1}+\frac{y^{2}}{4}=1$
$\Rightarrow \quad \frac{x^{2}}{(1)^{2}}+\frac{y^{2}}{(2)^{2}}=1$
which is also an equation of ellipse with $a=1$ and $b=2$
Hence, there is no intersecting point.
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