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10-2. Parabola, Ellipse, Hyperbola
normal
Number of points on the ellipse $\frac{{{x^2}}}{{50}} + \frac{{{y^2}}}{{20}} = 1$ from which pair of perpendicular tangents are drawn to the ellips $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{9}} = 1$
A
$0$
B
$2$
C
$1$
D
$4$
Solution
For the ellipse $\frac{\mathrm{x}^{2}}{16}+\frac{\mathrm{y}^{2}}{9}=1$ equation of director circle is $x^{2}+y^{2}=25 .$
This director circle will cut the ellipse $\frac{\mathrm{x}^{2}}{50}+\frac{\mathrm{y}^{2}}{20}=1$ at $4$ points hence number of points $=4.$
Standard 11
Mathematics