Acircle is centered at (2,-5) and has radius 3. write its equation in standard form.
a)
(x + 2)2 + (y - 5)2 = 3
b)
(x - 2)2 + (y + 5)2 = 3
(x + 2)2 + (y - 5)2 = 9
(x - 2)² + (y + 5)² = 9

Option (D) is correct

Step-by-step explanation:

A circle has (a , b ) are the coordinates of the centre and .

Given.

A circle is centered at (2,-5) and has radius 3

Let and and

The standard form of the circle is.

------(1)

Put a, b and r value in equation  1.

So. the standard form of equation is.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12