Question

can you please solve:
obtain the equation of the tangent to the curve at YX^2=1, at point A(p,1/p2) if this tangent line cutting the x-axis at point B, and y-axis at point C. PROVE that CA=2AB.

Answer 1

that is p_2 not 2p, right?

Answer 2

yes

Answer 3

So CA means the dot product of C and A?
What kinda product is that?

Also I suppose you know to find the x-intercept and y-intercept of the tangent line?

Answer 4

yes but CA is where C is a point at the y-axis and A is a point at the curve of the tangent, i did't get you about what's the product?
no, how?

Answer 5

I don't know what CA=2AB means? I know what everything else means.
But C, A and B are points.

Answer 6

I can help you with everything before CA=2AB but then I can't go further unless I know the notation of what CA=2AB means.

Did you find y' yet?

Answer 7

i think we have to obtain the area of the tangent if i'm not mistaken. that's what CA=2AB maybe
no i didn't find y' yet, if you can please solve it

Answer 8

You have yx^2=1
You could solve for y first.
Then find the derivate.

Answer 9

\[y=\frac{1}{x^2}\]
Take derivative of both sides.

Answer 10

y2x=0
d/dx(yx^2)=d/dx(1)
y2x=0
2xy=0 so?

Answer 11

\[(yx^2)'=y(x^2)'+(y)'x^2 \text{ use product rule} \]

Answer 12

ok, and then...

Answer 13

Find y'.

Answer 14

To find the slope of the tangent line going through (p,1/p2) evaluate y' at that point.

Answer 15

thanks myininaya for making things clear, even though i didn't solve it because i still have another thing to do.. i really appreciate your help. Thank you

Answer 16

Ok so you know to find the equation of the tangent line.
Find the x and y intercept of that equation.
You should be able to show that equality whatever that equality means because I still have no clue what CA=2AB means.

Answer 17

yeah, i'll do my best to finish it.. me too i don't know

Answer 18

Refer the drawing for the question asked. The curve is not exactly Y.X^2 = 1.

Answer 19

Take a point A (p, 1/p^2) and find the equation of tangent for the given curve at that point. Find y intercept, x intercept and then find the distance between x intercept and the tangent point (AB) and find the distance between Y intercept and the tangent point ( AC ). Then prove AB = 2 x AC

Answer 20

Oh so AB is the distance of from point A to B.
We can't do your work for you.

Answer 21

This problem won't take very long since we know what AC=2*AB means now.

Answer 22

hhhh, actually thats what i said at the begining "we have to find the area"

Answer 23

He said distance, not area.

Answer 24

almost the same

Answer 25

Entirely different.