If the line ax + y = c, touches both the curves x2 + y2 = 1 and y2 = 4[ 2 ]x , then |c| is…

Question

If the line ax + y = c, touches both the curves x2
 + y2
 = 1 and y2
 = 4$$\sqrt 2 $$x , then |c| is equal to :

Accepted Answer

Tangent to the curve y2 = 4$$\sqrt 2$$x is y = mx + $${{\sqrt 2 } \over m}$$

It is tangent to the circle x2 + y2 = 1

$$ \therefore $$ $$\left| {{{\sqrt 2 /m} \over {\sqrt {1 + {m^2}} }}} \right| = 1 \Rightarrow m =  \pm 1$$

$$ \therefore $$  tangent are y = x + $$\sqrt 2$$ \& y = -- x -- $$\sqrt 2$$

Compare with y = -- ax + c

$$ \Rightarrow a =  \pm 1 $$ \& $$ c =  \pm \sqrt 2 $$

Solutions · 1