Mathematics - Online Test

y = m x + c ---(i)

y2=4ax ---(ii)

putting the value of y from (i) in (ii), we get

(mx+c)2=4ax

=> (mx)2+x(2mc−4a)+c2=0

here

discriminant =(2mc−4a)2−4m2c2−−−−−−−−−−−−−−−−−√

                     =16a2−16amc−−−−−−−−−−−√

when discriminant >0 line touches parabola at two points,

when discriminant < 0 line do not  touches parabola and

when discriminant = 0 line touches parabola at one point

and we know that tangent is a line that touches the curve at exactly one point

so putting discriminat = 0 and solving

we get c=am,m≠0

on putting the value of y from line in the parabola and solving for equal roots.

If there are n objects to be arranged in circular order the no of permutations possible=(n−1)!

First we will make the 5 girls around the table and this can be done in (5−1)!=4!=24 , different ways

Now  we have 5 places available between these girls and the 5 boys can be seated in these 5 available places in 5!=120, different ways

Hence the 5 boys and 5 girls can be arranged in 4!.5!=24.120=2880ways