Maths

Please can u help me with this question
22) C is a circle with centre the origin.
A tangent to C passes through the points (–20, 0) and (0, 10)
Work out an equation of C.
You must show all your working.

Reply 1

ghostwalker

Original post by raidas0001

What have you done so far, and where are you stuck?

Reply 2

raidas0001

Original post by ghostwalker

What have you done so far, and where are you stuck?

x^2+y^2=r^2
gradint=(10-0)/(0--20)=0.5
y=mx+c
y=0.5x+c
0=0.5(-20)+c
0=-10+c
c=10
y=0.5x+10
1/2 x -2 =-1
y=2x+c
10=2(0)+c
c=10
r=2x+10

Reply 3

ghostwalker

Original post by raidas0001

x^2+y^2=r^2
gradint=(10-0)/(0--20)=0.5
y=mx+c
y=0.5x+c
0=0.5(-20)+c
0=-10+c
c=10
y=0.5x+10

I can see here that you're worked out the equation of the tangent.

1/2 x -2 =-1

Looks is if you're finding the gradient of a perpendicular line

y=2x+c
10=2(0)+c
c=10
r=2x+10

Your gradient seems to have changed from -2 to 2.

And you're finding a perpendicular line going through (0,10). Don't think that's going to be very useful.

If you want the perpendicular to be a radius, then it needs to go through the centre of the circle - viz. the origin.

You might find a diagram helpful, if you haven't already drawn one.

I presume you're then finding the intersection of the two lines, and hence the radius?