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

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

ion

step-by-step explanation:

ion ion ion ion ion ion ion ion ion ion ion