10.2 parabola,ellipse,hyperbola — ગણિત ધોરણ 11 સાયન્સ — Question

For this equation to represent an ellipse its eccentricity shoule lie between 0 and 1 .

$\sqrt{1-\frac{b^2}{a^2}} < 1$

$0 < 1-\frac{(4-a)^2}{(10-a)^2} < 1$

$0 < (10-a)^2-(4-a)^2 < 1$

$0 < 84-12 a < 1$

$0 < (7-a) 12 < 1$

$12(7-a) > 0$ and

$12(7-a) < 1$

$a < 7$ and $7- a < \frac{1}{12}$

$a < 7 \text { and } a > \frac{83}{12}$