Let $x,y$ be real variable satisfying the $x^{2} + y^{2} + 8x - 10y - 40 = 0$. Let $a = \max\left( \

Question

Let $x,y$ be real variable satisfying the $x^{2} + y^{2} + 8x - 10y - 40 = 0$. Let $a = \max\left( \sqrt{(x + 2)^{2} + (y - 3)^{2}} \right)$ and $b = min\left( \sqrt{(x + 2)^{2} + (y - 3)^{2}} \right)$, then:

Accepted Answer

[Key Concept: $a,b$ are (centre-distance to $( - 2,3)$)$\pm$ radius: max/min of $(x{+ 2)}^{2} + (y{- 3)}^{2}$ over the circle.]$$\begin{matrix} & a = 9 + 2\sqrt{2} \ & b = 9 - 2\sqrt{2} \ & ab = 81 - 8 = 73 \ & a + b = 18 \ & a - b = 4\sqrt{2} \end{matrix}$$

Question

Options

Solution

More Circle Questions