Which equation describes the circle having center point (4,2) and radius r= 3 in standard form?

ANSWER

EXPLANATION

The standard equation of a circle with center (h,k) and radius r is given by :

We were given the center (4,2) and radius r=3.

We substitute the center and radius into the equation to obtain:

This simplifies to:

Hence the equation of the circle in standard form is

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

idk

step-by-step explanation: