If the minimum area of the triangle formed by | vedclass

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

Question

Tangent

$\frac{x \cos 	heta}{b}+\frac{y \sin 	heta}{2 a}=1$

So, area $(\Delta \mathrm{OAB})=\frac{1}{2} 	imes \frac{\mathrm{b}}{\cos 	heta}

Vedclass · Accepted Answer

$2$

Vedclass · Answer

Tangent

$\frac{x \cos 	heta}{b}+\frac{y \sin 	heta}{2 a}=1$

So, area $(\Delta \mathrm{OAB})=\frac{1}{2} 	imes \frac{\mathrm{b}}{\cos 	heta} 	imes \frac{2 \mathrm{a}}{\sin 	heta}$

$=\frac{2 \mathrm{ab}}{\sin 2 	heta} \geq 2 \mathrm{ab}$

$\Rightarrow \mathrm{k}=2$

If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1$ and the co-ordinate axis is $kab,$ then $\mathrm{k}$ is equal to ..... .

Similar Questions

The length of the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{2}=1$, whose mid-point is $\left(1, \frac{1}{2}\right)$, is:

In the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, the equation of diameter conjugate to the diameter $y = \frac{b}{a}x$, is

The equation of tangent and normal at point $(3, -2)$ of ellipse $4{x^2} + 9{y^2} = 36$ are

The latus rectum of an ellipse is $10$ and the minor axis is equal to the distance between the foci. The equation of the ellipse is

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is