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
RBI has proposed to revise the definition of bulk deposits as a ‘Single Rupee term deposit of _______’ for Scheduled Commercial Banks. Â
...When was the Hindustan Republican Association formed?
____________ is an order or order given by a superior court to a subordinate court or tribunal or public authority if it is not discharging its duty.
Which of the following banks is the TV broadcast sponsor for Indian Team In Asian Games?
Which bollywood actor ranked fourth in the list of the highest paid actors 2019 according to Forbes?
Which of the following pairs represents biodegradable materials?
Forest Research Institute of India is located at _________.
Which pond in Rudraprayag is traditionally believed to be the confluence point of the streams of the Ganga and Yamuna rivers?
Where was the 48th International Film Festival of India held in 2017?
According to the 2011 Census of India, which state has the highest population in India?
Relevant for Exams:
