Need help with this calculus question

I have completed part a of this question but I'm stuck on part b. Can anyone help me with this part?

Attach the question

How do I attach an image?

idk ab that, i use a laptop... but if you can type out the question?

There’s a diagram on the question

How do I attach an image?

oh um.... did you get it from a website? is there a link?

if the tangent is at 45 degrees, whats the gradient at those points?

-1

So sub it in to the gradient equation and get a relationship for y in terms of x, then sub that into the equation of the ellipse and solve for x (and then y)

I managed to do part B. For the coordinates of A(-2root10, -root10) and B(2root10, root10)

Not worked it through, but looks plausible and easy enough to verify by subbing back in.

okay thanks. For part C would I just use the formula for distance between two points

Looks like it. The "hence ..." and 2 marks is about right for pythagoras.

I have completed part a of this question but I'm stuck on part b. Can anyone help me with this part?

Since part a) was a show that question, you will need to use that for part b).
Points A and B are the points of inflection. Points of inflection are defined as ‘curve changing from concave to convex, and when second differential is zero’.
So you: differentiate again, set it equal to 0 and find the x coordinates. Proof it is a point of inflection by substituting numbers into the second differential just below and just above the x values. You should get a positive (convex) and negative (concave) values. Than find the y values.