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10-2. Parabola, Ellipse, Hyperbola
normal
A tangent is drawn to the ellipse $\frac{{{x^2}}}{{32}} + \frac{{{y^2}}}{8} = 1$ from the point $A(8, 0)$ to touch the ellipse at point $P.$ If the normal at $P$ meets the major axis of ellipse at point $B,$ then the length $BC$ is equal to (where $C$ is centre of ellipse) - ............ $\mathrm{units}$
A
$1$
B
$2$
C
$3$
D
$4$
Solution
$\frac{x^{2}}{32}+\frac{y^{2}}{8}=1$
from property
$\mathrm{CB} \cdot \mathrm{CA}=(\mathrm{CS})^{2}$
$=a^{2}-b^{2}$ (where $\mathrm{S}$ is focus of ellipse)
$\Rightarrow \quad \mathrm{CB} \cdot 8=32-8$
$\mathrm{CB}=\frac{24}{8} \Rightarrow \mathrm{CB}=3 \text { units }$
Standard 11
Mathematics
