Mathematics - Online Test

Because line joining the points (a, 0) and (0, b)  will be diameter and it's mid-point will be centre of the circle.

Or let the equation of circle be (x−h)2+(y−k)2=r2

as circle passes through  (0,0) , (a,0) and (0,b), they will satisfy the above equation

putting the points in above equation we get

h2+k2=r2

(a−h)2+k2=r2  ---(ii)

h2+(b−k)2=r2 ---(iii)

Solving (i) and (ii),we get  h=a2

whereas solving (i) and (iii) we get k=b2

hence its center is (a2,b2)

he value of cosθ$\cos \theta$  lies between - 1 and 1 

But when t=2 the value of   cosθ=1+t21−t2,t≠0$\cos \theta =\frac{1+t^2}{1-t^2},t\ne 0$ is 5−3 which is more than 1 , so it is not possible.

Let P(α,β,γ) be the point and Q (0,b,0) be any point on Y axis.

drs of PQ=(α,β−b,γ)

drs of y axis (0,b,0)

Since PQ perpendicular to y axis.hence a1a2+b1b2+c1c2=0

hence the foot of perpendicular will be (0,β,0)

wehave3600=24.32.52

To get the odd factors we will get rid of 2's

We will make the selection from only 3's and 5's 

Number of ways 3 can be selected from a lot of two 3's= 3 ways ( one 3,two 3's or three 3's)

Number of ways 5 can be selected from a lot of two 5's= 3 ways ( one 5,two 5's or three 5's)

Therefore  the number of odd factors is 3600= 3 X 3 =9