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P Pankaj Sanodiya
Since the Axis of the parabola is vertical, Let the equation of the parabola be,  it can be seen that this curve will pass through the point (5/2, 10) if we assume origin at the bottom end of the parabolic arch. So, Hence, the equation of the parabola is  Now, when y = 2 the value of x will be  Hence the width of the arch at this height is 

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P Pankaj Sanodiya
Given, in a hyperbola,  Foci , passing through (2,3) Since foci of the hyperbola are in Y-axis, the equation of the hyperbola will be of the form ; By comparing standard parameter (foci) with the given one, we get Now As we know, in a hyperbola  Now As the hyperbola passes through the point (2,3) Solving Equation (1) and (2) Now, as we know that in a hyperbola  is always greater...

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P Pankaj Sanodiya
Given, in a hyperbola vertices (± 7,0), And   Here, Vertices is  on the X-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (Vertices and eccentricity) with the given one, we get  and  From here, Now, As we know the relation  in a hyperbola  Hence, The Equation of the hyperbola is ;

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P Pankaj Sanodiya
Given, in a hyperbola Foci (± 4, 0), the latus rectum is of length 12 Here,  focii are on the X-axis so, the standard equation of the Hyperbola will be ; By comparing standard parameter (length of latus rectum and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Since  can never be negative, Hence, The Equation of the hyperbola is ;

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P Pankaj Sanodiya
Given, in a hyperbola Foci , the latus rectum is of length 8. Here,  focii are on the X-axis so, the standard equation of the Hyperbola will be ; By comparing standard parameter (length of latus rectum and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Since  can never be negative, Hence, The Equation of the hyperbola is ;

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P Pankaj Sanodiya
Given, in a hyperbola Foci (0, ±13), the conjugate axis is of length 24. Here, focii are on the Y-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (length of conjugate axis and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Hence, The Equation of the hyperbola is ; .

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P Pankaj Sanodiya
Given, in a hyperbola Foci (± 5, 0), the transverse axis is of length 8. Here,  focii are on the X-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (transverse axis length and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Hence, The Equation of the hyperbola is ;

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P Pankaj Sanodiya
Given, in a hyperbola  Vertices (0, ± 3), foci (0, ± 5) Here, Vertices and focii are on the Y-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (Vertices and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Hence, The Equation of the hyperbola is ; .

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P Pankaj Sanodiya
Given, in a hyperbola Vertices (0, ± 5), foci (0, ± 8) Here, Vertices and focii are on the Y-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (Vertices and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Hence, The Equation of the hyperbola is ; .

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P Pankaj Sanodiya
Given, in a hyperbola Vertices (± 2, 0), foci (± 3, 0) Here, Vertices and focii are on the X-axis so, the standard equation of the Hyperbola will be ; By comparing the standard parameter (Vertices and foci) with the given one, we get  and  Now, As we know the relation  in a hyperbola  Hence,The Equation of the hyperbola is ;

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as   Comparing this equation with the standard equation of the hyperbola: We get,  and  Now, As we know the relation in a hyperbola, Therefore, Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as  Comparing this equation with the standard equation of the hyperbola: We get,    and  Now, As we know the relation in a hyperbola, Here as we can see from the equation that the axis of the hyperbola is Y-axis. So,  Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as  Comparing this equation with the standard equation of the hyperbola: We get,  and  Now, As we know the relation in a hyperbola, Therefore, Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as  Comparing this equation with the standard equation of the hyperbola: We get,  and  Now, As we know the relation in a hyperbola, Hence,  Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as  Comparing this equation with the standard equation of the hyperbola: We get,  and  Now, As we know the relation in a hyperbola, Here as we can see from the equation that the axis of the hyperbola is Y-axis. So,  Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :

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P Pankaj Sanodiya
Given a Hyperbola equation, Can also be written as  Comparing this equation with the standard equation of the hyperbola: We get,  and  Now, As we know the relation in a hyperbola, Here as we can see from the equation that the axis of the hyperbola is X -axis. So,  Coordinates of the foci: The Coordinates of vertices: The Eccentricity: The Length of the latus rectum :
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