![\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{4}=1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79b83cfd05141077d859b528a32f1b5d_l3.png "Rendered by QuickLaTeX.com")
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 (v)...
conjugate axis is \[7\]and passes through the point \[\left( 3,\text{ }-2 \right)\] Given: Conjugate axis \[=\text{ }7\] Passes through the point \[\left( 3,\text{ }-2 \right)\] Conjugate axis is...
(i) the distance between the \[foci\text{ }=\text{ }16\text{ }and\text{ }eccentricity\text{ }=\text{ }\surd 2\] Given: Distance between the foci \[=\text{ }16\] Eccentricity \[=\text{ }\surd 2\] Let...
\[{{x}^{2}}-\text{ }3{{y}^{2}}-\text{ }2x\text{ }=\text{ }8\] Given: The equation \[=>\text{ }{{x}^{2}}-\text{ }3{{y}^{2}}-\text{ }2x\text{ }=\text{ }8\] Let us find the centre, eccentricity,...
(i) \[16{{x}^{2}}-\text{ }9{{y}^{2}}~+\text{ }32x\text{ }+\text{ }36y\text{ }-\text{ }164\text{ }=\text{ }0\] Given: The equation \[=>\text{ }16{{x}^{2}}-\text{ }9{{y}^{2}}~+\text{ }32x\text{...
Given: The equation\[=>\text{ }25{{x}^{2}}-\text{ }36{{y}^{2}}~=\text{ }225\] The equation can be expressed as: The obtained equation is of the form Where, \[a\text{ }=\text{ }3\text{ }and\text{...
\[2{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }5\] Given: The equation \[=>\text{ }2{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }5\] The equation can be expressed as: The obtained equation is of the form...
(i) \[4{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }36\] Given: The equation \[=>\text{ }4{{x}^{2}}-\text{ }3{{y}^{2}}~=\text{ }36\] The equation can be expressed as: The obtained equation is of the...
(i) \[9{{x}^{2}}-\text{ }16{{y}^{2}}~=\text{ }144\] Given: The equation \[=>\text{ }9{{x}^{2}}-\text{ }16{{y}^{2}}~=\text{ }144\] The equation can be expressed as: The obtained equation is of the...
(i) \[focus\text{ }is\text{ }\left( a,\text{ }0 \right),\]\[directrix\text{ }is\text{ }2x\text{ }+\text{ }3y\text{ }=\text{ }1\]and \[eccentricity\text{ }=\text{ }2\] Given: \[Focus\text{ }=\text{...
(i) \[focus\text{ }is\text{ }\left( 1,\text{ }1 \right)\]\[directrix\text{ }is\text{ }2x\text{ }+\text{ }y\text{ }=\text{ }1\] and \[eccentricity\text{ }=\surd 3\] Given: \[Focus\text{ }=\text{...
(i) focus is \[\left( 0,\text{ }3 \right),\] directrix is \[x\text{ }+\text{ }y\text{ }-\text{ }1\text{ }=\text{ }0\] and eccentricity \[=\text{ }2\] Given: Focus \[=\text{ }\left( 0,\text{ }3...
Given: The equation of the directrix of a hyperbola \[=>\text{ }x\text{ }-\text{ }y\text{ }+\text{ }3\text{ }=\text{ }0\] Focus \[=\text{ }\left( -1,\text{ }1 \right)\] and Eccentricity \[=\text{...