Find the equations of both lines that pass through the origin and are tangent to the parabola y =x² + 4

Question

anonymous · Answer

first lets call the points $$P(a_{1},b_{1}),Q(a,b)$$

anonymous · Answer

their gradient is
$$f \prime (x)=2x$$

anonymous · Answer

since they are passing through the origin they have the equation
$$y=2(a)x$$
$$y=2(a _{1})x$$

anonymous · Answer

all we have to do now is find the points intersection with the graph

anonymous · Answer

$$a^2+4=2(a)a$$

dumbcow · Answer

lines tangent to parabola have slope of 2x

y=mx+b
since they must go through origin, b=0 
--> y = (2x)*x = 2x^2
find point where
x^2 +4 = 2x^2
--> x = +-2

therefore 2 lines are
y = +-4x

anonymous · Answer

$$2a^2-a^2=4$$
$$a^2=4$$
$$x=\pm 2$$

anonymous · Answer

very nice dumbcow

anonymous · Answer

y cordinate$$y=2(2)=4$$
$$y=2(-2)=-4$$