Question

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

Answer 1

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

Answer 2

their gradient is
\[f \prime (x)=2x\]

Answer 3

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

Answer 4

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

Answer 5

\[a^2+4=2(a)a\]

Answer 6

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

Answer 7

\[2a^2-a^2=4\]
\[a^2=4\]
\[x=\pm 2\]

Answer 8

very nice dumbcow

Answer 9

y cordinate\[y=2(2)=4\]
\[y=2(-2)=-4\]