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10-2. Parabola, Ellipse, Hyperbola
normal
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
A
$x^2 + y^2 = 5$
B
$\sqrt 5$ $(x^2 + y^2) - 3x - 4y = 0$
C
$ \sqrt 5$ $(x^2 + y^2) + 3x + 4y = 0$
D
$x^2 + y^2 = 25$
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