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

whatever you can spend with $11.53 or under.

step-by-step explanation:

20 - 8.47 = 11.53. take away the money he used for lunch from the starting amount of 20.