The coordinate of a point on the auxiliary ci | vedclass

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

Question

(B) The given equation of the ellipse is $x^{2}+2y^{2}=4$. Dividing by $4$,we get $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$. Comparing this with the standar

Vedclass · Accepted Answer

$(1, \sqrt{3})$

Vedclass · Answer

(B) The given equation of the ellipse is $x^{2}+2y^{2}=4$. Dividing by $4$,we get $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$. Comparing this with the standard form $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$,we have $a^{2}=4$,so $a=2$. The auxiliary circle of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is given by $x^{2}+y^{2}=a^{2}$. Here,the equation of the auxiliary circle is $x^{2}+y^{2}=4$. The coordinates of a point on the auxiliary circle corresponding to an eccentric angle $	heta$ are given by $(a \cos 	heta, a \sin 	heta)$. Given $	heta = 60^{\circ}$ and $a=2$,the coordinates are $(2 \cos 60^{\circ}, 2 \sin 60^{\circ})$. Substituting the values,we get $(2 	imes \frac{1}{2}, 2 	imes \frac{\sqrt{3}}{2}) = (1, \sqrt{3})$. Thus,the correct option is $B$.

The coordinate of a point on the auxiliary circle of the ellipse $x^{2}+2y^{2}=4$ corresponding to the point on the ellipse whose eccentric angle is $60^{\circ}$ will be

Similar Questions

The area of the quadrilateral formed by the tangents at the end points of the latus rectum to the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$ is .............. $sq. \text{ units}$.

If tangents are drawn to the ellipse $x^2+2y^2=2$,then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is

Let $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b)$ be a given ellipse whose latus rectum length is $10$. If its eccentricity $e$ is the maximum value of the function $\phi(t) = \frac{5}{12} + t - t^{2}$,then $a^{2} + b^{2}$ is equal to:

The eccentricity of an ellipse passing through $(3 \sqrt{2}, \sqrt{10})$ with foci at $(-4,0)$ and $(4,0)$ is

The locus of the midpoints of the segments of the tangents to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ intercepted between the coordinate axes is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module