Circles Past Paper questions

Hey!
I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
a)find the coordinates of A and the radius of C
b)The line L has equation x-3y+4=0
Show that L is a tangent to circle C

Reply 1

Bored123454321

1

Original post by alicebrr

Hey!
I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
a)find the coordinates of A and the radius of C
b)The line L has equation x-3y+4=0
Show that L is a tangent to circle C

to show that something is a tangent you must put the equation of the line into the equation of the circle and show that it only meets the circle at one point. If this is the case it will usually factorize into 2 identical brackets

Reply 2

Bored123454321

1

Original post by alicebrr

Hey!
I have been sat here trying this question for at least 2 hours and tried everything I can think of...any ideas? (it's part b I am stuck on, but I will put entire question up)

Question: The circle C has centre A and equation x^2+y^2+4x-8y+10=0
a)find the coordinates of A and the radius of C
b)The line L has equation x-3y+4=0
Show that L is a tangent to circle C

so for part b i would make y the subject of the equation of the line, put it into the equation of the circle, expand and simplify, make it equal 0 and it should factorise into 2 identical brackets from which you can say that because there is only 1 solution that it is a tangent

Reply 3

the bear

20

part a)

expand

( x - a )² + ( y - b )² = r²

and compare to your version to find a,b,r

Reply 4

alicebrr

OP

7

Original post by Bored123454321

so for part b i would make y the subject of the equation of the line, put it into the equation of the circle, expand and simplify, make it equal 0 and it should factorise into 2 identical brackets from which you can say that because there is only 1 solution that it is a tangent