Ellipse 4x^2 + 9y^2 = 36 and hyperbola 4x^2 -y^2 = 4 have same foci and they intersect

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10-2. Parabola, Ellipse, Hyperbola

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The ellipse $ 4x^2 + 9y^2 = 36$ and the hyperbola $ 4x^2 -y^2 = 4$ have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

$x^2 + y^2 = 5$

$\sqrt 5$ $(x^2 + y^2) - 3x - 4y = 0$

$ \sqrt 5$ $(x^2 + y^2) + 3x + 4y = 0$

$x^2 + y^2 = 25$

Solution

Add the two equations to get $8$ $\left( {x_1^2\, + \,y_1^2\,} \right)$ $= 40$
$\Rightarrow$$x_1^2\, + \,y_1^2$ $ = 5$ $ \Rightarrow $ $r = \sqrt 5 \,$

Standard 11

Mathematics

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The ellipse $ 4x^2 + 9y^2 = 36$ and the hyperbola $ 4x^2 -y^2 = 4$ have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

Solution

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