Question

How to find all points P on the parabola y = x^2
such that the tangent line at P passes through the
point ( 0, 4 )?? What if the point were changed to ( 2, 5 ) ?

Answer 1

doesn't look possible to me

Answer 2

o.O its a homework question...so i hope its possible

Answer 3

are sure you wrote the problem correctly?

Answer 4

eh sorry! (0,-4)

Answer 5

can't see how to draw a line though (0,4) tangent to the curve. maybe my thinking is off

Answer 6

then (2,-5) :/ sorry

Answer 7

ok so you know that the derivative of
\[y=x^2\] is
\[y'=2x\] and therefore any point on the curve
\[(x,x^2)\] that is tangent has to satisfy
\[2x=\frac{x^2+4}{x-0}\]

Answer 8

that is the slopes must match up

Answer 9

solve this equation for x to get your answer

Answer 10

\[2x^2=x^2+4\]
\[x^2=4\]
\[x=\pm2\] so you have two lines tangent to the curve at (0,-4)

Answer 11

the one through

\[(2,4),(0,-4)\] and the one through
\[(-2,4) ,(0,-4)\]

Answer 12

second one is the same. solve
\[2x=\frac{x^2+5}{x-2}\]for x

Answer 13

im a little confused on how you get those equations where 2x=x^2+5/x-2 and the other