Part $1$: The function $f(x,y)=arccos(x^2+y^2-10)is$ defined only when $x^2+y^2,$ where:

$=$

$=$

$In$ the $xy-$plane, the interval found above $is$ equivalent $to$ the region:

inside a circle with radius $\sqrt[\phantom{2}]{}$ including the points $on$ the circumference.

between concentric circles with radii $\sqrt[\phantom{2}]{}$ and $\sqrt[\phantom{2}]{}$ including both circumferences.

inside a circle with radius $and$ outside a circle with radius $$

between a set $of$ perpendicular lines with slopes $+-\sqrt[\phantom{2}]{\frac{}{}}$

Part $2$: For $z(x,y)=ln(3x^2+2y^2-6),$ write down the condition that needs $to$ hold for $(x,y)tobein$

the domain $ofz.$

The table $at$ the bottom $of$ the question may $be$ helpful.

$(i)$ Condition:

$(ii)$ What type $of$ conic section $is$ involved $in$ the domain $ofz?$

Ellipse

Circle

Hyperbola

$(iii)If$ you sketch that conic section $in$ the $xy-$plane, then what points will make $up$ the domain $ofz?$

Interior $of$ the conic section excluding the points $on$ the curve.

Exterior $of$ the conic section excluding the points $on$ the curve.

Interior $of$ the conic section including the points $on$ the curve.

Exterior $of$ the conic section including the points $on$ the curve.