Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)
Solution and Explanation
Vertices (±2, 0), foci (±3, 0)
Here, the vertices are on the x-axis.
Therefore, the equation of the hyperbola is of the form \(\frac{x^2}{a^2} –\frac{ y^2}{b^2} = 1\).
Since the vertices are (±2, 0), a = 2.
Since the foci are (±3, 0), c = 3.
We know that \(a ^2 + b^ 2 = c^ 2.\)
\(∴ 2^2 + b^2 = 3^2\)
\(b^2 = 9 – 4 = 5\)
∴ The equation of the hyperbola is \(\frac{x^2}{4} –\frac{ y^2}{5} = 1\)
Top CBSE Class XI Mathematics Questions
- A coin is tossed twice, what is the probability that atleast one tail occurs?
- The relation f is defined by
\(f(x) = \begin{cases} x^2, & \quad 0≤x≤3\\ 3x, & \quad 3≤x≤10 \end{cases}\)
The relation g is defined by
\(g(x) = \begin{cases} x^2, & \quad 0≤x≤2\\ 3x, & \quad 2≤x≤10 \end{cases}\)
Show that f is a function and g is not a function. - Let \(f={(x,\frac {x^2}{1+x^2}):x∈R}\) be a function from R into R. Determine the range of f.
- How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
- In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
Top CBSE Class XI Questions
- The total number of protons in $ 10\,g$ of calcium carbonate is $ (N_{0}=6.023\times 10^{23})$ :
- Justify giving reactions that among halogens, fluorine is the best oxidant and among hydrohalic compounds, hydroiodic acid is the best reductant.
- An oxygen cylinder of volume 30 litre has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol–1 K–1, molecular mass of O2 = 32 u).
- Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm pressure.
- An air bubble of volume 1.0 cm3 rises from the bottom of a lake 40 m deep at a temperature of 12 °C. To what volume does it grow when it reaches the surface, which is at a temperature of 35 °C ?
Concepts Used:
Hyperbola
Hyperbola is the locus of all the points in a plane such that the difference in their distances from two fixed points in the plane is constant.
Hyperbola is made up of two similar curves that resemble a parabola. Hyperbola has two fixed points which can be shown in the picture, are known as foci or focus. When we join the foci or focus using a line segment then its midpoint gives us centre. Hence, this line segment is known as the transverse axis.
