Question

what is $4\sqrt{a(1+m^{2})(c+am^2 )}$ ?

Answer 1

Answer:

Given equation of line

y=mx+c

Given the equation of a parabola

y

2

=4a(x+a)

⇒(mx+c)

2

=4ax+4a

2

⇒m

2

x

2

+(2mc−4a)x+(c

2

−4a

2

)=0

Since line touches the parabola i.e. there is only one solution.

⇒D=0

⇒(2mc−4a)

2

−4m

2

(c

2

−4a

2

)=0

⇒mc=a(1+m

2

)

⇒c=

m

a(1+m

2

)

⇒c=

m

a

+am