The coordinates of the foci of the ellipse 16 | vedclass

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

Question

(B) Given the equation of the ellipse: $16x^{2} + 9y^{2} = 144$. Dividing both sides by $144$,we get: $\frac{16x^{2}}{144} + \frac{9y^{2}}{144} = 1$,w

Vedclass · Accepted Answer

$(0, \pm \sqrt{7})$

Vedclass · Answer

(B) Given the equation of the ellipse: $16x^{2} + 9y^{2} = 144$. Dividing both sides by $144$,we get: $\frac{16x^{2}}{144} + \frac{9y^{2}}{144} = 1$,which simplifies to $\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1$. Comparing this with the standard form $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$,we have $a^{2} = 9$ and $b^{2} = 16$. Since $b^{2} > a^{2}$,the major axis is along the $y$-axis. Here,$a = 3$ and $b = 4$. The eccentricity $e$ is given by $e = \sqrt{1 - \frac{a^{2}}{b^{2}}} = \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4}$. The coordinates of the foci are $(0, \pm be) = (0, \pm 4 	imes \frac{\sqrt{7}}{4}) = (0, \pm \sqrt{7})$.

The coordinates of the foci of the ellipse $16x^{2} + 9y^{2} = 144$ are

Similar Questions

The ellipse $E_1: \frac{x^2}{9} + \frac{y^2}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_2$ circumscribes the rectangle $R$ and passes through the point $(0, 4)$. What is the eccentricity of the ellipse $E_2$?

If the normal at any point $P$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ meets the coordinate axes in $G$ and $g$ respectively,then $PG:Pg = $

$A$ focus of an ellipse having eccentricity $e = \frac{1}{2}$ is at $(0,0)$ and a directrix is the line $x = 4$. Then the equation of one such ellipse is

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $\frac{x^{2}}{100}+\frac{y^{2}}{400}=1$.

The mid-point of a chord of the ellipse $x^2+4y^2-2x+20y=0$ is $(2,-4)$. The equation of the chord is

Vedclass Test Series

Exam Paper Generator

Online Exam Module