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Circle Tangent questions.

I am having a fair bit of trouble getting the correct answers for a few questions in my math book

Find the equations of the tangents to the circle x^2+y^2+6x-2y-15=0 that are perpendicular to the line 4x+3y+5=0

Find the equations of the tangent fromt he given point to the given circle.

Point (0,0) Circle x^2-y^2+4x+2y+4=0

Tried to get the answer for these for the last half an hour but failed to do so.
Reply 1
Avatar for TenOfThem
TenOfThem
18
For the first one you are looking for a line

You know the gradient of the line but not the intercept so you will still have +c in the equation

Then you substitute that line into the circle equation ... then you will have a quadratic in x

You are looking for a single solution so the discriminant = 0



For the other one the meted is basically the same but in your equation of a line you know c but not m
Reply 2
Avatar for Coulson72
Coulson72
first find the general form of the perpandicular to the circle so you have ax+by=c.
rearrange for y= whatever
substitute y into your circle and you want the discriminant to be equal to 0, so that for the x there in only once y possible (the discriminant should be a quadractic in c so solve this equation) :wink:

for this second one find the formula of the line first and you should get y=kx.
substitute this in to find the two possible values of k using a similar method :biggrin:
Reply 3
Avatar for Sgany
Sgany
OP
12
Got the second question still having trouble on the 1st.
(edited 12 years ago)
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by Sgany
Tried those methods and got no results so far.


No

me neither

is the question correct
Reply 5
Avatar for Sgany
Sgany
OP
12
Original post by TenOfThem
No

me neither

is the question correct


Probably not the maths book is pretty crap and full of mistakes :frown: I will talk to my teacher tomorrow about it.
Reply 6
Avatar for Repressor
Repressor
11
The point (0,0) doesn't lie on the circle.

EDIT: Whoops, wrong circle.
EDIT2: Well the second one isn't even a circle, it's a hyperbola?
EDIT3: Still doesn't lie on it even if it was a circle...
(edited 12 years ago)
Reply 7
Avatar for iamben
iamben
Original post by Sgany
I am having a fair bit of trouble getting the correct answers for a few questions in my math book

Find the equations of the tangents to the circle x^2+y^2+6x-2y-15=0 that are perpendicular to the line 4x+3y+5=0

Is line 4x+3y+5=0 a tangent to the circle? If so then a line perpendicular to it would go through the centre of the circle. You can use the equation of the circle to find that using completing the square. Then you just need to work out the gradient of the tangent to the circle and insert it all into y-y1=m(x-x1).
Is this what you're looking for?
(edited 12 years ago)

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