Find an equation of the hyperbola that satisfies the given conditions . Foci (0, +4) one vertex (0,-2) 5. Center at (-2,-4); a vertex at (-2,-7); a focus at (-2,-9) 6. Ends of conjugate axis at (3,5) and (3,-1); eccentricity
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Given that,
Ends of the conjugate axis is at
Here the centre of the hyperbola is in the midpoint of
Therefore the mid point of two points is given by
Therefore the mid point of is
So, the centre of the hyperbola is .
Therefore the origin is shifted to .
Let be the coordinates of the point with respect to the new axis.
Therefore,
Therefore ends of the conjugate axis is
Therefore
Since the conjugate axis is in y-axis, the foci is in x- axis.
Since the eccentricity, is given by
Then
Therefore the hyperbola is
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