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10-1.Circle and System of Circles
normal
Number of integral points interior to the circle $x^2 + y^2 = 10$ from which exactly one real tangent can be drawn to the curve $\sqrt {{{\left( {x + 5\sqrt 2 } \right)}^2} + {y^2}} \, - \sqrt {{{\left( {x - 5\sqrt 2 } \right)}^2} + {y^2}\,} \, = 10$ are (where integral point $(x, y)$ means $x, y \in I)$
A
$12$
B
$14$
C
$16$
D
$18$
Solution
All the points must lie in the shaded figure where $|y| \geq|x|$ and equality holds if $x>0$ such that $\mathrm{x}^{2}+\mathrm{y}^{2}<10$
Standard 11
Mathematics
