If the vertices and foci of a hyperbola are respectively $$( pm 3,0)$$ and $$( pm 4,0)$$, then the parametric equations of that hyperbola are

$$x=3 sec heta, y= sqrt{7} an heta$$

$$x= sqrt{3} sec heta, y= sqrt{7} an heta$$

$$x= sqrt{3} sec heta, y=7 an heta$$

Let origin be the centre, $$( pm 3,0)$$ be the foci and $$ frac{3}{2}$$ be the eccentricity of a hyperbola. Then, the line $$2 x-y-1=0$$

does not intersect the hyperbola.

intersects the hyperbola at two points.

passes through the vertex of the hyperbola.

The length of the latusrectum of an ellipse is $$ frac{18}{5}$$ and eccentricity is $$ frac{4}{5}$$, then equation of the ellipse is .....

$$ frac{x^2}{25}+ frac{y^2}{9}=1$$

$$ frac{x^2}{25}+ frac{y^2}{8}=1$$

$$ frac{ dot{x}^2}{25}+ frac{y^2}{16}=1$$

$$ frac{x^2}{16}+ frac{y^2}{9}=1$$

The focal distance of the point $$(x, y)$$ from the ellipse $$ frac{x^2}{a^2}+ frac{y^2}{b^2}=1, a>b$$ is

$$a pm sqrt{1- frac{b^2}{a^2}} x$$

$$a pm sqrt{1- frac{b^2}{a^2}} y$$

$$b pm sqrt{1- frac{a^2}{b^2}} y$$

$$b pm sqrt{1- frac{a^2}{b^2}} x$$

Conic Section 3

Last Updated :

Discuss

Comments

Question 1

If the vertices and foci of a hyperbola are respectively [Tex]( \pm 3,0)[/Tex] and [Tex]( \pm 4,0)[/Tex], then the parametric equations of that hyperbola are

[Tex]x=3 \sec \theta, y=7 \tan \theta[/Tex]
[Tex]x=\sqrt{3} \sec \theta, y=\sqrt{7} \tan \theta[/Tex]
[Tex]x=\sqrt{3} \sec \theta, y=7 \tan \theta[/Tex]
[Tex]x=3 \sec \theta, y=\sqrt{7} \tan \theta[/Tex]

Discuss it

Question 2

Let origin be the centre, [Tex]( \pm 3,0)[/Tex] be the foci and [Tex]\frac{3}{2}[/Tex] be the eccentricity of a hyperbola. Then, the line [Tex]2 x-y-1=0[/Tex]

intersects the hyperbola at two points.
does not intersect the hyperbola.
touches the hyperbola.
passes through the vertex of the hyperbola.

Discuss it

Question 3

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

[Tex]\frac{1}{\sqrt{2}}[/Tex]
[Tex]\frac{2 \sqrt{2}}{3}[/Tex]
[Tex]\frac{2}{\sqrt{3}}[/Tex]
[Tex]\frac{1}{\sqrt{3}}[/Tex]

Discuss it

Question 4

The equations of the directrices of the elmpse [Tex]9 x^2+4 y^2-18 x-16 y-11=0[/Tex] are

[Tex]y=2 \pm \frac{9}{\sqrt{5}}[/Tex]
[Tex]x=1 \pm \frac{6}{\sqrt{5}}[/Tex]
[Tex]x=2 \pm \frac{9}{\sqrt{5}}[/Tex]
[Tex]y=1 \pm \frac{6}{\sqrt{5}}[/Tex]

Discuss it

Question 5

If the area of the ellipse is [Tex]\frac{x^2}{25}+\frac{y^2}{\lambda^2}=1[/Tex] is [Tex]20 \pi[/Tex] sq units, then [Tex]\lambda[/Tex] is

[Tex]\pm 4[/Tex]
[Tex]\pm 3[/Tex]
[Tex]\pm 2[/Tex]
[Tex]\pm 1[/Tex]

Discuss it

Question 6

If [Tex]e_1[/Tex] and [Tex]e_2[/Tex] are the eccentricities of the hyperbola [Tex]16 x^2-9 y^2=1[/Tex] and its conjugate respectively. Then, [Tex]3 e_1=[/Tex]

[Tex]5 e_2[/Tex]
[Tex]4 e_2[/Tex]
[Tex]2 e_2[/Tex]
[Tex] e_2[/Tex]

Discuss it

Question 7

The length of the latusrectum of an ellipse is [Tex]\frac{18}{5}[/Tex] and eccentricity is [Tex]\frac{4}{5}[/Tex], then equation of the ellipse is .....

[Tex]\frac{x^2}{25}+\frac{y^2}{8}=1[/Tex]
[Tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/Tex]
[Tex]\frac{\dot{x}^2}{25}+\frac{y^2}{16}=1[/Tex]
[Tex]\frac{x^2}{16}+\frac{y^2}{9}=1[/Tex]

Discuss it

Question 8

The eccentricity of the ellipse [Tex]y^2+4 x^2-12 x+6 y+14=0[/Tex] is

[Tex]\frac{1}{\sqrt{2}}[/Tex]
[Tex]\frac{1}{2}[/Tex]
[Tex]\frac{\sqrt{3}}{2}[/Tex]
[Tex]\frac{1}{\sqrt{3}}[/Tex]

Discuss it

Question 9

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola [Tex]x^2-y^2=a^2[/Tex] is

[Tex]y^4-x^4=4 a^2 x^2 y^2[/Tex]
[Tex]y^2-x^2=4 a^2 x^2 y^2[/Tex]
[Tex]a^2\left(y^2-x^2\right)=4 x^2 y^2[/Tex]
[Tex]y^2+x^2=4 a^2 x^2 y^2[/Tex]

Discuss it

Question 10

The focal distance of the point [Tex](x, y)[/Tex] from the ellipse [Tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b[/Tex] is

[Tex]a \pm \sqrt{1-\frac{b^2}{a^2}} y[/Tex]
[Tex]b \pm \sqrt{1-\frac{a^2}{b^2}} y[/Tex]
[Tex]a \pm \sqrt{1-\frac{b^2}{a^2}} x[/Tex]
[Tex]b \pm \sqrt{1-\frac{a^2}{b^2}} x[/Tex]

Discuss it

Tags:

Mathematics

School Learning

There are 10 questions to complete.

Take a part in the ongoing discussion