# Thread: Sums of x and y intercerpts of any tangent line to the curve

1. ## Sums of x and y intercerpts of any tangent line to the curve

can anyone help me with this question?

Prove that the sum of the x and y intercepts of any tangent line to the curve x^1/2 + y^1/2 = k^1/2 is constant and is equal to k.

2. Originally Posted by rawrzjaja
can anyone help me with this question?

Prove that the sum of the x and y intercepts of any tangent line to the curve x^1/2 + y^1/2 = k^1/2 is constant and is equal to k.
First get the equation of the tangent at to the curve at x = a. Can you do that?

3. Originally Posted by mr fantastic
First get the equation of the tangent at to the curve at x = a. Can you do that?
Once you do this, solve for both the x and y intercepts. Add them together. They should be equal to k.

4. not too sure how to get x = a... sry T_T, can you show me please

5. Originally Posted by rawrzjaja
not too sure how to get x = a... sry T_T, can you show me please
In more detail: What I've suggested is find the tangent at the general point (a, b) where b is related to a via the equation for the curve.