
first n natural numbers are 1,2,3.....n
we know that,
sum of sqaure is

The line which is parallel to X axis and crosses the curve y = at an angle of is:
The equation of the line which is a tangent to the curve y = is
y = mx + a/m
Since it makes and angle of 450, m = 1
y2 = x implies a = 1/4
Hence the equation of the tangent is y = x+
That is the y intercept is = 1/2
Hence the equation of the line is y = 1/2
Let Y=y and X = x-a
for standard parbola Y2=4aX the vertex is (0,0)
so put X=0 and Y=0.
i.e. put x-a = 0 and y=0
so vertex is (a,0)
