COMEDK Exam 2016 Solved Paper

Let the equation of line by y=mx+C
Since, this is the tangent to the circle x2+y2=5
So, C‌=±a√1+m2
‌=±√5√1+m2 . . . (i)
Also, the above line is tangent to the parabola
‌y2=40x
So, ‌c=‌

a

m

=‌

10

m

. . . (ii)

By Eqs. (i) and (ii), we get
‌

10

m

‌=±√5√1+m2
m4+m2−20‌=0
(m2+5)(m2−4)‌=0
m2‌=4(m2≠−5)
m‌=±2⇒c=±5
‌ Here, ‌‌‌y‌=±2x±5←