Conic Sections MATHS - Conic Sections

The length of the latus rectum of the ellipse 3x² + y² = 12 is:

1. 4
2. 3
3. 8
4. $\frac{4}{\sqrt{3}}$

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is:

1. x² + y² = 9a²
2. x² + y² = 16a²
3. x² + y² = 4a²
4. x² + y² = a²

[Hint: Centroid of the triangle coincides with the centre of the circle and the radius of the circle is $\frac{2}{3}$ of the length of the mediam]

If e is the eccentricity of the ellipse $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1(\text{a}<\text{b}),$ then:

1. b² = a²(1 - e²)
2. a² = b²(1 - e²)
3. a² = b²(e² - 1)
4. b² = a²(e² - 1)