Question

show the graphs 2x^2+y^2=6 and y^2=4x intersect by showing that the slopes of the tangents are opposite reciprocals at (1,2)

Answer 1

You must find the equation of the tangent of the circle at (1,2) and then do the same for the parabola. And then the same for the parabola. And if the gradients of the tangents multiply to give negative one, (their reciprocal made negative), then the two graphs intersect.

When I say negative reciprocal, if one graph has a gradient of 2. Then the other tangent would need to be -1/2. (If the graphs intersect then their tangents straight line equation will be perpendicular to eachother and is theory for the above statement).

Answer 2

first one is not a circle... it's an ellipse i think

Answer 3

okay, thanks

Answer 4

http://www.wolframalpha.com/input/?i=2x^2%2By^2%3D6+and+y^2%3D4x

Looks like a circle to me.

Answer 5

if you were to divide by 6 to get the one side one.. you'd get 3 under one and 6 under the other..

i believe it looks like a circle because the square root of 6 and 3 are less than 1 in difference

Answer 6

you could also solve for y to change it into a x function that you can take the derivative of which will the slope will be your derivative at that point

Answer 7

It looks like a circle because the x and y axes are not at the same scale. Very misleading.

I fail to see how the tangents being perpendicular means that the graphs intersect. I can give examples of graphs that intersect where their tangents aren't perpendicular. For example, y=1 and y=x.

Answer 8

i believe that the question states that at the point it is perpendicular

Answer 9

but really in another case you'd be totally correct as they don't have to be perpendicular

Answer 10

Ok. Maybe revolver left a word out.

Here's another example that really demonstrates the axis scale problem: http://www.wolframalpha.com/input/?i=100x^2%2By^2%3D6+and+y^2%3D4x