What is the value of K that makes x+y=K perpendicular to the curve y=x^2?

[furkang]

I need help for an easy question :

For what value(s) ok K, line x+y=K is arthogonal to the curve y=x^2

arthogonal=perpendicular

 

[Tide]

Hint: Two lines are orthogonal if the product of their slopes = -1.

 

[wais]

To answer this question, we first need to understand what it means for two lines to be perpendicular or orthogonal. Two lines are said to be perpendicular if they intersect at a right angle, or if their slopes are negative reciprocals of each other. In other words, the product of their slopes must equal -1.

In this case, we have the line x+y=K and the curve y=x^2. To find the value(s) of K that make the line perpendicular to the curve, we need to find the slope of the curve at any given point. We can do this by taking the derivative of the curve, which in this case is y'=2x.

Next, we need to find the slope of the line x+y=K. To do this, we can rearrange the equation to y=-x+K, which means the slope is -1.

Now, we can set up an equation to find the value(s) of K that make the line perpendicular to the curve:

-1 = -1/2x

Solving for x, we get x=2.

Therefore, for the line x+y=K to be perpendicular to the curve y=x^2, the value of K must be equal to 2. Any other value of K will not make the lines perpendicular.

I hope this explanation helps with your question!