Find the equation of hyperbola whose foci are (0, ) and passing through the point (2, 3).
since Foci is on the y-axis, the required equation of hyperbola is
Now co-ordinates of foci = (0, ) and given foci =
So,
a2 = b2(e2 - 1) = b2e2 - b2
a2 = 10 - b2
Equation of hyperbola becomes,
9a2 - 40 + 4a2 = 10a2 - a4
a2 can not be negative.
We get, b2 = 5
the required equation is
Show that the rectangle of maximum perimeter which can be inscribed in a circle o radius 10 cm is a square of side 10 cm.
Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white and four black balls. A dice having three red, two yellow, and one green face, is thrown to select the box. If red face turns up, we pick up box I, if yellow face turns up, we pick up box II, otherwise we pick up box III. Then, we draw a ball from the selected box. If the ball drawn is white, what is the probability that the dice had turned up with a red face?
Five dice are thrown simulteneously. If the occurence of an odd number in a single dice is considered a success, find the probability of maximum three successses.