DLS
  • DLS
Find the equation of the tangent to the curve at the given point and show that the sum of its intercepts on its axes is constant
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DLS
  • DLS
\[\Huge \sqrt{x}+\sqrt{y}=\sqrt{a}, point~(x_1,y_1)\]
DLS
  • DLS
Attempt: \[\LARGE \frac{dy}{dx}=- \sqrt{\frac{y_0}{x_0}}\] \[\LARGE (y-y_0)= - \sqrt{\frac{y_0}{x_0}}(x-x_0)\] don't know if this equation is correct or not but my ans is wrong
anonymous
  • anonymous
Your solution is ok, maybe is wrong becuase you have used (xo, yo) instead of (x1,y1) as stated in the problem

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anonymous
  • anonymous
A question of notation, I guess...
DLS
  • DLS
its x1,y1 only sorry and no i didn't even mean that..answer is completely different..
DLS
  • DLS
\[\LARGE \frac{x}{\sqrt{x_1}}+\frac{y}{\sqrt{y1}}=\sqrt{a}\] is the answer..
DLS
  • DLS
I am not even getting "a" in my answer o_O i wonder how they are getting
DLS
  • DLS
@ganeshie8
DLS
  • DLS
but what about the tangent !
ganeshie8
  • ganeshie8
actually your equation is exact same as the answer you just need to simplify @DLS
ganeshie8
  • ganeshie8
\(\large y-y_1 = -\sqrt{\frac{y_1}{x_1}}(x-x_1)\) divide \(\sqrt{y_1}\) both sides \(\large \frac{y}{\sqrt{y_1}}-\frac{y_1}{\sqrt{y_1}} = -\sqrt{\frac{1}{x_1}}(x-x_1)\) \(\large \frac{y}{\sqrt{y_1}}-\frac{y_1}{\sqrt{y_1}} = -\frac{x}{\sqrt{x_1}} + \sqrt{x_1}\) \(\large \frac{y}{\sqrt{y_1}} + \frac{x}{\sqrt{x_1}} = \frac{y_1}{\sqrt{y_1}} + \sqrt{x_1}\) \(\large \frac{y}{\sqrt{y_1}} + \frac{x}{\sqrt{x_1}} = \sqrt{y_1} + \sqrt{x_1}\) \(\large \frac{y}{\sqrt{y_1}} + \frac{x}{\sqrt{x_1}} = \sqrt{a}\)

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