A circle with centre at the point (2,-1) passes through the point A at (4,-5). (a) Find an equation for the circle C.

(b) Find an equation of the tangent to the circle C at the point A, giving your answer in the form ax+by+c=0, where a, b, and c are integers..

a)

b)

Step-by-step explanation:

a) the centre is (2,-1)

the equation so far is:

because you just change the sign of 2 to -2 and change the sign of -1 to +1

to find the radius:

to find diameter square 2√5

b) find the gradient between the points (2,-1) and (4,-5)

the gradient of the tangent is the negative reciprocal of -2. This means you flip it upside down which would be -1/2, then multiply by -1 which is 1/2

the gradient is 1/2

using the gradient and the point (4,-5) to write the equation in the form y=mx+c

here y is -5, m is the gradient (1/2) and x is 4

we need to work out c

subtract 2 on both sides

now the equation is

but we need to write it in the form ax+by+c=0

subtract y on both sides:

multiply everything by 2 to get rid of the fraction

that is the final equation

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.