lol maths help (1 Viewer)

[1610839335]

okok well i was just doing my tutor hw
and i stumbled upon an unfamiliar question..
not quite sure how to work it out.
Any help is much appreciated x]

Show that the line 3x+4y+10=0 is a tangent to the circle with centre at the origin and radius 2 units.

 

[inconnuBubble]

Get the equation for the circle first...ie: x^2 + y^2 = 4
Then solve that and 3x + 4y + 10 = 0 simultaneously
3x + 4y + 10 = 0
x = (-10 - 4y) / 3
sub x into x^2 + y^2 = 4
(100 + 16y^2 - 80y) / 9 + y^2 = 4
25y^2 + 80y + 64 = 0
*delta* = b^2 - 4ac
= 6400 - 6400
= 0
Since the discriminant is equal to 0
*therefore* there is one root
*therefore* 3x + 4y + 10 = 0 is a tangent to the circle x^2 + y^2 = 4

 

[1610839335]

THANKS BUBBLE SAMA



*ahem* george