Conics Q (1 Viewer)

[nrlwinner]

Find the equation of the tangent at the point (3,-4) to the circle x^2+y^2=25.

I got the answer to be 3x-4y=25

What are the equations of the two tangets parallel to the y-axis?

I got x=5 and x=-5

Show that the first tanget intersects these tangets in points which subtend a right angle at the origin.

 

[shaon0]

Find the equation of the tangent at the point (3,-4) to the circle x^2+y^2=25.

I got the answer to be 3x-4y=25

What are the equations of the two tangets parallel to the y-axis?

I got x=5 and x=-5

Show that the first tanget intersects these tangets in points which subtend a right angle at the origin.

2x+2yy'=0
-x/y=y'
At (3,-4): y'=3/4

y+4=3/4.(x-3)
y=(3/4)x-25/4
4y=3x-25
3x-4y=25

At x=5: y=-5/2 and At x=-5: y=-10
m1= (-5/2)/5 = -1/2 and m2= (-10)/(-5)=2
m1m2=-1

 

[nrlwinner]

Thanks. I've got another one here.

I've figured out that x^2+y^2=16 and x^2+y^2-24x-10y+88=0 touch each other externally.

How do I show that 24x+10y-104=0 is a common tangent

 

[untouchablecuz]

Thanks. I've got another one here.

I've figured out that x^2+y^2=16 and x^2+y^2-24x-10y+88=0 touch each other externally.

How do I show that 24x+10y-104=0 is a common tangent