equation of circle / tangents

The line y+4x=k is a tangent of a circle

a)substitute y=k-4x into the equation of the circle x^2 +y^2=17

i get x^2 +k^2-8kx+16x^2=17

b) write down the condition for the equation to have coincident roots

c)solve the quadratic equation in k to give the 2 values of k and hence the equations of the 2 possible tangents

Reply 1

Cortez

edit: hmmm i think i got it wrong :redface:

Reply 2

Meat Loaf Rocks

Cortez

hmmm i think i got it wrong :redface:

join the club

Reply 3

geekypoo

No he is right, its kx

Reply 4

Cortez

Your answer to part a) is right i think. I worked it out and got -8x instead of -8kx but ive done it again and got -8kx.

Im not sure about the others :/

Reply 5

mizfissy815

I think it should be 16x^2...not 16x

Reply 6

mizfissy815

so it should be 17x² +k² -8kx

Reply 7

Meat Loaf Rocks

fisfos815

so it should be 17x² +k² -8kx

yes sorry for that error,
can you do part b and c

Reply 8

geekypoo

Well for this shouldnt you find the derivative of the circle and find when the gradient = 4

x^2 + y^2 -17 = 0
2x + 2y(dy/dx) =0
dy/dx = -2x/2y

So when dy/dx = 4
-2x = 8y
y= -¼x

-¼x= k-4x

x= 4/15 k

x^2 +k^2-8kx+16x²=17
(16/225)k² + k² - 32/15 k² +256/225k²-17=0

16k²+225k²-480k² +256k²-3825=0
17k²-3825=0

k²= 3825/17= 225
k= √225 = ±15