# Line not intersecting circle, maximum value of expression involving radius

If line $$y+x=2$$ do not intersect any member of circles $$x^2 + y^2 -ax = 0$$ at two distinct points where a is parameter, then maximum value of $$|a + 4|$$.

My try: Since the line does not intersect the circle at 2 distinct points therefore the distance of line from center of circle is greater than or equal to the radius of the circle

Circle is $$x^2 + y^2 -ax = 0$$ therefore its radius is $$a$$ and center is $$(a, 0)$$

Distance of line $$x^2 + y^2 -ax = 0$$ from center of circle is given by $$\frac{|a - 2|}{\sqrt2}$$

Therefore we get the inequality $$\frac{|a - 2|}{\sqrt2} \ge a$$

But I can't find a way to solve it further to obtain the maximum value of |a + 4|

• Try to find values of $a$ such that line and circle are tangent. Jul 16, 2014 at 7:18

• I'm not entirely sure how you came up with that expression. For one thing, the circle's centre is actually at $(\frac{a}{2}, 0)$ and its radius is actually $\frac{a}{2}$. Jul 16, 2014 at 8:54