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)