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1. If y is a real function of the real variable x defined by
x^2+ y^2-6x-8y=0
Then find the range of the function y.
2. A1,A2.A3,... are points in the first quadrant on the parabola
y^2=4x. If the x co ordinates of the points be in HP. the first two being 1, 1/2 then the y co ordinate of the point An is______?
x2 -6x + y2 - 8y = 0
(x2-6x+9) + (y2-8y+16) = 25
(x-3)2 + (y-4)2 = 25
(y-4) = [ 25 - (x-3)2]1/2
y = [25 - (x-3)2]1/2 + 4
maximum value of this function is when x = 3
y = 9
minimum value of this function is when x = 8
y = 4
range = [4,9]
it repesents a circle with centre (3,4) and radius 5 .max value is 4+5 = 9
y^2 = 4x =============== yn = 2root(xn) xn = 1/(1+(n-1)) =============== xn = 1/n ============== yn = 2/root(n)
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