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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______?

10 years ago

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]

10 years ago

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)