Download App

Ellipse — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsEllipse1 Mark
Question
Write the centre and eccentricity of the ellipse $3\text{x}^2+4\text{y}^2-6\text{x}+8\text{y}-5=0.$
✓

Answer

$\Rightarrow3\text{x}^2-6\text{x}+4\text{y}^2+8\text{y}-5=0$
$\Rightarrow3(\text{x}^2-2\text{x})+4(\text{y}^2+2\text{y})=5$
$\Rightarrow3(\text{x}^2-2\text{x}+1)+4(\text{y}^2+2\text{y}+1)=5+3+4$
$\Rightarrow3(\text{x}-1)^2+4(\text{y}+1)^2=12$
$\Rightarrow\frac{3(\text{x}-1)^2}{12}+\frac{4(\text{y}+1)^2}{12}=1$
$\Rightarrow\frac{(\text{x}-1)^2}{4}+\frac{(\text{y}+1)^2}{3}=1$
Compairing it with $\frac{\text{x}^2}{\text{b}^2}+\frac{\text{y}^2}{\text{b}^2}=1,$ we get:
a = 2 and $\text{b}=\sqrt{3}$
Here, a > b, so the major and the minor axes of the ellipse are along the x−axis and y−axis, respectively.
Now, $\text{e}=\sqrt{1-\frac{\text{b}^2}{\text{a}^2}}$
$\Rightarrow\text{e}=\sqrt{1-\frac{3}{4}}$
$\Rightarrow\text{e}=\sqrt{\frac{1}{4}}$
$\therefore\ \text{e}=\frac{1}{2}$ and centre = (1, -1)

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Ellipse→Ellipse — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.

{(1, 3), (4, 1), (2, 2)}

→
Write the number of diagonals of an n-sided polygon.
→
Which of the following relations are functions? If it is a function determine its domain and range.

{(0, 0), (1, 1), (1, -1), (4, 2), (4, -2) (9, 3), (9, -3), (16, 4), (16, -4)}

→
Write the conjugates of the following complex numbers: cos θ + i sin θ
→
Write down the all possible proper subset of the given set.
{1, 2}
→
Which of the following statements are true and which are false? In each case give a valid reason for saying so:
q: The centre of a circle bisects each chord of the circle.
→
Examine the continuity of :
$f(x)=\frac{x^2-9}{x-3}$, for $x \neq 3$
$=8$ for $x=3$, at $x=3$.
→
Write the distance between the lines $4x + 3y - 11 = 0$ and $8x + 6y - 15 = 0$.
→
Write the coordinates of the foot of the perpendicular from the point (1, 2, 3) on y-axis.
→
Find the degree measure corresponding to the following radian measures: $(\text{Use}\ \pi=\frac{22}{7})$
$\frac{9\pi}{5}$
→