Ellipse: In the ellipse, the distance between its foci is 6 and minor axis is… | AIEEE 2006 | Yukti Vault

Yukti Vault

AIEEE 2006 (Offline)Question 1

In the ellipse, the distance between its foci is $6$ and minor axis is $8$. Then its eccentricity is :

Ellipse

$\frac35$✓ Correct answer$\frac12$$\frac45$$\frac{1}{\sqrt5}$

Solution

Formulas used. (1) $a^2=b^2+c^2$, $e=\frac ca$Step 1 - Data. $2c=6\Rightarrow c=3$; $2b=8\Rightarrow b=4$. Step 2 - Use (1). $a=\sqrt{16+9}=5$, $e=\frac35$. Answer: A

More from Ellipse

Let O(0,0) and A(0,1) be two fixed points. Then, the locus of a point P such that the perimeter of Delta AOP…
On the ellipse fracx^28+fracy^24=1 let P be a point in the second quadrant such that the tangent at P to the…
Let the length of the latus rectum of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , (a>b) , be 30 . If its…
Let A be the point (3,0) and circles with variable diameter AB touch the circle x^2+y^2=36 internally. Let…
Let (x^2)/(a^2)+(y^2)/(b^2)=1 ( a>b ) be a given ellipse, length of whose latus rectum is 10 . If its…
The radius of the circle passing through the foci of the ellipse dfracx^216+dfracy^29=1 , and having its…
Find the equation of the common tangent in the 1^st quadrant to the circle x^2+y^2=16 and the ellipse…
Let a focus of the ellipse E:fracx^2a^2+fracy^2b^2=1 be S(4,0) and its eccentricity be frac45 . If the point…