- Home
- Standard 11
- Mathematics
10-2. Parabola, Ellipse, Hyperbola
normal
If a number of ellipse be described having the same major axis $2a$ but a variable minor axis then the tangents at the ends of their latera recta pass through fixed points which can be
A
$(0, a)$
B
$(0, - a)$
C
$(0, 0)$
D
both $(A)$ and $(B)$
Solution
Equation of the ellipse is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
$x$ axis is the major axis Latus rectum co-efficient $\left(a e, \frac{b^{2}}{a}\right)$
Equation of tangent $\pm \frac{x}{a^{2}} a P \pm \frac{y}{b^{2}} \cdot \frac{b^{2}}{a}=1$
$\frac{P^{x}}{a}+\frac{y}{a}-1=0$
$P x+y-a=0$
$(y-a)+P x=0$
$L_{1}+\lambda L_{2}=0$
$y=a \quad x=0$
So, $(0, a)$ and $(0,-a)$
Standard 11
Mathematics
