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Show that the sum of the $ x- $ and $ y- $ intercepts of any tangent line to the curve $ \sqrt x + \sqrt y = \sqrt c $ is equal to $ c. $

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Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

if this problem were given any question of liquor and rest, show that some of intercepts off the kinds of plans for the security. Physical. See? So let's first find the question of times like you know that tension line will be performed. Ah y minus or not is equal to decorative. A boy who let God given point my sex once. It's not, unless it should not be regulating that. A foreign excited one. All right, now we're gonna differentiate both sides with respect, X So we have where we're screwed of x waas one over to spirit of why times why prime is a zero promise. Then we say that why farm is able to negative or Howard to spirit of X divided by one forward to skirt apply So that is equal to negative spirit of what he wanted. Five. Spergel Ex Act given point Why prime ist equal to negative skirt off. Why not you find a spirited off? It's no And from this you see that the question of 10 to 1 it will be for my minus or not is equal to negative skirt off, boy. Not the right spirit of excellent plans. X minus. That's not Oh now the females lie of both sides by I screwed it up. It's not. We find the question of stunned when mobile for extra mile but X not waas. Buried off excellent times. Why not? Plus one The wind it bugs her. Go um X not. And why not? Plus, why not His equal warm. So from this we see that then the intercepts or spread it off our X nine times. Why not? What sex? Not also spirit of extract times Why not Waas? What? Not now. Some of those too would then be X note Waas to skirt it up. Excellent plans. Why not? Plus why not? And that is he actually equal to some off ex snugs loss some point scoring right now. Look at this for so scary of except prospered a point and look at the origin of the question Now, if you were capable it this give any questions at a given point it's not going up. You would end up with a spirit of C, so that would be equal to the spirit of C squared, which is equal proceed. So we just showed that the sum of interceptor turns of mine is able to see