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...

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:...

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:...

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...

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:...

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:...

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:...

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:...

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...

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...

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,...

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,...

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,...

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,...

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,...

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,...

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,...

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, \[a=3,b=\sqrt{27}=3\sqrt{3}\]...

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, \[a=3,b=\sqrt{27}=3\sqrt{3}\]...

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, \[a=3,b=\sqrt{27}=3\sqrt{3}\]...

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...

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)...

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...

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

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

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

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

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...

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...

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...

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 = \[\frac{2{{b}^{2}}}{a}=2\]...

Given Equation: \[{{x}^{2}}-{{y}^{2}}=1\] Comparing with the equation of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] (iii) coordinates of the foci =\[(\pm ae,0)=(\pm...

Given Equation: \[{{x}^{2}}-{{y}^{2}}=1\] Comparing with the equation of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] (i)Length of Transverse axis = \[2a=2\]units. Length...

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)...

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...

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)...

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)...