A focus of an ellipse is at the origin. The d | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Obviously the major axis is along the $x$ -axis The distance between the focus and the

corresponding directrix $=\left|\frac{a}{e}-a e\right|=4$

Vedclass · Accepted Answer

$\frac{8}{3}$

Vedclass · Answer

Obviously the major axis is along the $x$ -axis The distance between the focus and the

corresponding directrix $=\left|\frac{a}{e}-a eight|=4$

$\left.\Rightarrow \frac{a}{e}-a e=4 \quad 	ext { (note that } \frac{a}{e}>a eight)$

$\Rightarrow a\left(\frac{1}{e}-eight)=4 \Rightarrow a\left(2-\frac{1}{2}ight)=4$

$\Rightarrow a \cdot \frac{3}{2}=4 	herefore a=\frac{8}{3}$

A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $ \frac{1}{2}$ . Then the length of the semi-major axis is

Similar Questions

The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is

Number of tangents to the circle $x^2 + y^2 = 3$ , which are normal to the ellipse $4x^2 + 9y^2 = 36$ , is

If the ellipse $\frac{ x ^{2}}{ a ^{2}}+\frac{ y ^{2}}{ b ^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2 \sqrt{6}}=1$ on the $y$-axis, then the eccentricity of the ellipse is

The eccentricity of the ellipse $25{x^2} + 16{y^2} = 100$, is

Equation of the ellipse with eccentricity $\frac{1}{2}$ and foci at $( \pm 1,\;0)$ is