Standard Equation of Ellipse

Q. Length of minor axis J6, foci(0, ± 6)16.

Q. 15.Length of major axis 26, foci (+ 5, 0)

Q. An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

Q. 20.Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

Q.

What is the length of latusrectum of the ellipse $16x^2+y^2=16?$

Q. 13.Ends of major axis ± 3, 0), ends of minor axis (0, ± 2)

Q. 14.Ends of major axis (0--/5 ), ends of minor axis (± 1, 0)

Q. Consider two points A and B on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$
circles are drawn having segments of tangents at A and B in between tangents at the two ends of major axis of ellipse as diameter, then the length of common chord of the circles is

1. 8
2. 6
3. 10
4. 

Q. 19.Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and

Q. 17.Foci (± 3、0), a = 4

Q.

If the line $x+2y+4=0$ cutting the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in points whose eccentric angles are ${30}^{\circ }$ and ${60}^{\circ }$ subtends a right angle at the origin then its equation is

1. $\frac{x^2}{8}+\frac{y^2}{4}=1$

2. $\frac{x^2}{16}+\frac{y^2}{4}=1$

3. $\frac{x^2}{4}+\frac{y^2}{16}=1$

4. none of these

Q. 7. 36x2 4y2 - 144

Q. The eccentricity of the ellipse 25x² + 16y² = 400 is
(a) 3/5
(b) 1/3
(c) 2/5
(d) 1/5

Q. An ellipse, with foci at $(0,2)$ and $(0,–2)$ and minor axis of length $4$, passes through which of the following points ?

1. $(2,\sqrt{2})$
2. $(1,2\sqrt{2})$
3. $(\sqrt{2},2)$
4. $(2,2\sqrt{2})$

Q. The equation of the ellipse, whose length of the major axis is $20$ and foci are $(0,\pm 5),$ is

1. $\frac{x^2}{10}+\frac{y^2}{5\sqrt{3}}=1$
2. $\frac{x^2}{25}+\frac{y^2}{100}=1$
3. $\frac{x^2}{75}+\frac{y^2}{100}=1$
4. $\frac{x^2}{10}+\frac{y^2}{25}=1$

Q. Find the coordinates of a point on $y$-axis which are at a distance of $5\sqrt{2}$ from the point $P(3,-2,5)$

Q. If the ellipse $\frac{x^2}{4}+\frac{y^2}{1}=1$ meet the ellipse $\frac{x^2}{1}+\frac{y^2}{a^2}=1$ in four distinct points and $a=b^2-10b+25$, then the value b does not satisfy

1. $(-\infty ,4)$
2. (4, 6)
3. $(6,-\infty )$
4. [4, 6]

Q.

Given standard equation of ellipse,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$,
with eccentricity $e$.
Match the following
$\begin{array}{cc}a)\text{Major axis}& i\left)2a\right(1-e^2)\\ b)\text{Minor axis}& ii)y=0\\ c)\text{Double ordinate}& iii)x=0\\ d)\text{Latus Rectum length}& iv)x=\frac{-a}{e}\\ & v)\sqrt{1-\frac{b^2}{a^2}}\end{array}$

1. $a=ii,b=iii,c=iii,d=i$

2. $a=v,b=ii,c=vi,d=i$

3. $a=ii,b=iv,c=iii,d=v$

4. $a=iii,b=ii,c=vi,d=i$

Q. 9. 4x9y2 36

Q. 4centreattheorigin:focionthexaxis

Q. 2.4 25

Q. Equation of the circle passing through the focii of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at $(0,3)$ is

1. $x^2+y^2-6y-7=0$
2. $x^2+y^2-6y+7=0$
3. $x^2+y^2-6y-5=0$
4. $x^2+y^2-6y+5=0$

Q. 5.49 36

Q. If $\frac{x^2}{3-\alpha }+\frac{y^2}{2}=1$ represents an ellipse whose major axis is along the $x-$axis, then the range of $\alpha$ is

1. $(1,\infty )$
2. $(-\infty ,1)$
3. $(-\infty ,-1)$
4. $(3,\infty )$

Q. how to draw an astroid which has a equation (x)^2/3 + (y)^2/3 = a^2/3

Q.

Given standard equation of ellipse,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$,
with eccentricity $e$
Match the following
$\begin{array}{cc}\text{a) Focus}& i\left)\right(ae,0)\\ \text{b) Directrix}& ii\left)\right(a,0)\\ \text{c) Eccentricity}& iii)x=\frac{a}{e}\\ \text{d) Vertices}& iv\left)\right(-ae,0)\\ & v)x=\frac{-a}{e}\\ & vi)\sqrt{1-\frac{b^2}{a^2}}\end{array}$

1. $a=i,iv,b=ii,v,c=vi,d=iii$

2. $a=i,b=ii,v,c=vi,d=iii$

3. $a=i,iv,b=iii,v,c=vi,d=ii$

4. $a=i,b=iii,v,c=vi,d=ii$

Q. A ray emitting from the point $(-3,0)$ is incident on the ellipse $16x^2+25y^2=400$ at point $P$ with an ordinate $4.$ If the equation of the reflected ray after first reflection is $4x+3y=k,$ then the value of $k$ is

1. $12$
2. $-12$
3. $9$
4. $-9$

Q. If a tangent of slope 2 of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is normal to the circle $x^2+y^2+4x+1=0$ then the maximum value of ab is

1. 4
2. 6
3. Can’t be found
4. 2

Q. The extremities of the latus rectum of an ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is

1. $(\pm \sqrt{7},\pm \frac{9}{4})$
2. $(\pm \sqrt{9},\pm \frac{16}{5})$
3. $(\pm 4,\pm \frac{25}{4})$
4. $(\pm 6,\pm \frac{4}{5})$

Q. Find the points on the $x$-axis, whose distances from the line $\frac{x}{3}+\frac{y}{4}=1$ are $4$ units.