RS Aggarwal class 11 Hyperbola

### Find the equation of the hyperbola whose vertices are     and the eccentricity is     . Also, find the coordinates of its foci.

Given: Vertices are $\left( \mathbf{0},\text{ }\pm \mathbf{3} \right)$ and the eccentricity is $\frac{4}{3}$ Need to find: The equation of the hyperbola and coordinates of foci. Let, the...

### Find the equation of the hyperbola with eccentricity     and the distance between whose foci is     .

Given: Eccentricity is $\sqrt{2}$, and the distance between foci is $16$ Need to find: The equation of the hyperbola. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola, the length of whose latus rectum is     and the eccentricity is     .

Given: The length of latus rectum is $4$, and the eccentricity is $3$ Need to find: The equation of the hyperbola. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola whose foci are     and the eccentricity is

Given: Foci is  $~\left( \pm \surd \mathbf{5}\text{ }\mathbf{0} \right)$  and the eccentricity is $\sqrt{\frac{5}{3}}$ Need to find: The equation of the hyperbola. Let, the equation of the...

### Find the equation of the hyperbola whose vertices are     and the eccentricity is     .

Given: Vertices are $~\left( \pm \mathbf{2},\text{ }\mathbf{0} \right)$ and the eccentricity is $2$ Need to find: The equation of the hyperbola. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola whose foci are     and the length of the latus rectum is     units.

Given: Foci are$(\pm 3\sqrt{5},0)$  the length of the latus rectum is $8$ units Need to find: The equation of the hyperbola. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola whose foci are     and the conjugate axis is of the length     . Also, find its eccentricity.

Given: Foci are $(\pm 5,0)$, the conjugate axis is of the length $8$ Need to find: The equation of the hyperbola and eccentricity. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola whose foci are     and the transverse axis is of the length     .

Given: Foci are $(\pm \sqrt{29},0)$, the transverse axis is of the length $10$ Need to find: The equation of the hyperbola. Let, the equation of the hyperbola be:...

### Find the equation of the hyperbola with vertices at     and foci at     .

Given: Vertices at $\left( \mathbf{0},\text{ }\pm \mathbf{5} \right)$ and foci at $\left( \mathbf{0},\text{ }\pm \mathbf{8} \right)$     Need to find: The equation of the hyperbola. Let, the...

### Find the equation of the hyperbola with vertices at     and foci at     .

Given: Vertices at $\left( \pm \mathbf{6},\text{ }\mathbf{0} \right)$ and foci at $\left( \pm \mathbf{8},\text{ }\mathbf{0} \right)$ Need to find: The equation of the hyperbola. Let, the...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given $5{{y}^{2}}-9{{x}^{2}}=36$ $\frac{{{y}^{2}}}{36/5}-\frac{{{x}^{2}}}{4}=1$ Comparing with the equation of hyperbola  $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given $5{{y}^{2}}-9{{x}^{2}}=36$ $\frac{{{y}^{2}}}{36/5}-\frac{{{x}^{2}}}{4}=1$ Comparing with the equation of hyperbola  $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices 5y2 – 9×2 = 36

Given $5{{y}^{2}}-9{{x}^{2}}=36$ $\frac{{{y}^{2}}}{36/5}-\frac{{{x}^{2}}}{4}=1$ Comparing with the equation of hyperbola  $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given:$3{{y}^{2}}-{{x}^{2}}=108$ $\frac{{{y}^{2}}}{36}-\frac{{{x}^{2}}}{108}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given:$3{{y}^{2}}-{{x}^{2}}=108$ $\frac{{{y}^{2}}}{36}-\frac{{{x}^{2}}}{108}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given:$3{{y}^{2}}-{{x}^{2}}=108$ $\frac{{{y}^{2}}}{36}-\frac{{{x}^{2}}}{108}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given:$3{{y}^{2}}-{{x}^{2}}=108$ $\frac{{{y}^{2}}}{36}-\frac{{{x}^{2}}}{108}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get,...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given : $\frac{{{y}^{2}}}{9}-\frac{{{x}^{2}}}{27}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get, $a=3,b=\sqrt{27}=3\sqrt{3}$...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given : $\frac{{{y}^{2}}}{9}-\frac{{{x}^{2}}}{27}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get, $a=3,b=\sqrt{27}=3\sqrt{3}$...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given : $\frac{{{y}^{2}}}{9}-\frac{{{x}^{2}}}{27}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ We get, $a=3,b=\sqrt{27}=3\sqrt{3}$...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation: $\frac{{{y}^{2}}}{16}-\frac{{{x}^{2}}}{49}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ we get, $a=4,b=7$ (v) Length...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given Equation: $\frac{{{y}^{2}}}{16}-\frac{{{x}^{2}}}{49}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ we get, $a=4,b=7$ (iii)...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given Equation: $\frac{{{y}^{2}}}{16}-\frac{{{x}^{2}}}{49}=1$ Comparing with the equation of hyperbola $\frac{{{y}^{2}}}{{{a}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}}=1$ we get, $a=4,b=7$ (i)Length...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation: $24{{x}^{2}}-25{{y}^{2}}=600$⇒ $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1$ Comparing with the equation of hyperbola...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given Equation: $24{{x}^{2}}-25{{y}^{2}}=600$⇒ $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1$ Comparing with the equation of hyperbola...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given Equation: $24{{x}^{2}}-25{{y}^{2}}=600$⇒ $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{24}=1$ Comparing with the equation of hyperbola...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation:  $25{{x}^{2}}-9{{y}^{2}}=225$⇒ $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{25}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given Equation:  $25{{x}^{2}}-9{{y}^{2}}=225$⇒ $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{25}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given Equation:  $25{{x}^{2}}-9{{y}^{2}}=225$⇒ $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{25}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation:$3{{x}^{2}}-2{{y}^{2}}=6$ $\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1$ Comparing with the equation of hyperbola  $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ We...

### Find the (iii)Coordinates of the foci, (iv) eccentricity

Given Equation:$3{{x}^{2}}-2{{y}^{2}}=6$ $\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1$ Comparing with the equation of hyperbola  $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ We...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given Equation:$3{{x}^{2}}-2{{y}^{2}}=6$ $\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1$ Comparing with the equation of hyperbola  $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ We...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation: ${{x}^{2}}-{{y}^{2}}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ (v) Length of the rectum = $\frac{2{{b}^{2}}}{a}=2$...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given Equation: $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{4}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 5 and b = 2 (iii)...

### Find the (i) lengths of the axes, (ii) coordinates of the vertices

Given Equation: $\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{4}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 5 and b = 2...

### Find the (v) length of the rectum of each of the following the hyperbola :

Given Equation: $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 3 and b = 4 (v)...

### Find the (iii) coordinates of the foci, (iv) eccentricity

Given Equation: $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 3 and b = 4 (iii)...

Given Equation: $\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{16}=1$ Comparing with the equation of hyperbola $\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$ we get, a = 3 and b = 4 (i)...