Question
If a hyperbola passes through the point (4, 0) and has
foci at (±5, 0), and the length of its conjugate axis is 6, then the eccentricity is:Solution
The hyperbola has foci at (±5,0), which means the center of the hyperbola is at the origin (0,0) and the major axis lies along the x-axis. The distance from the center to each focus is c. So, c=5. The length of the conjugate axis is 2b=6, which implies b=3. For a hyperbola, the relationship between a, b, and c is c2 = a2 + b2 Substituting the values of b and c:
52 = a2 + 32
a = 4 The equation of the hyperbola with center at the origin and major axis along the x-axis is 
The point (4,0) indeed lies on the hyperbola. This also means that the vertex of the hyperbola along the positive x-axis is at (4,0), so a=4, which is consistent with our calculation. The eccentricity e of a hyperbola is defined as e=c/a​. Substituting the values of c and a: e = 5/4
the following question the relationship between different elements is given in the statements followed by two conclusions given below. Decide which of...
Statements: D = P > Q = X ≤ Y = M; J = X; K > Q
Conclusion: I. M > K II. M ≤ K
Statements:Â
A $ B % D % CÂ
Conclusions:Â
I. B © CÂ
II. A * DÂ
III. C % A
Statements: A = C > G > H = B > O; E < P = R > B
Conclusions:
I). Â E > H
II).  H ≤ E
...In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
Statements: M ≥ G > K = Y; A ≥ Z ≥ E > M = I
Conclusions:
I. A ≥ I
II. K < E
III. I > G
Statements: R ≥ S = T; R < U < V; W > X > V
Conclusion:
I. U > T
II. T < V
Statements: R > N > Z < O = I ≥ T < W < S ≤ L
Conclusion
I: L > Z
II: O > T
Statement: E < N < Q = W = F ≥ U > A
Conclusion:
I. Q > A
II. E > F
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