Question

the point on the curve x^2/9+y^2/25=1 where tangent is parallel to x axis are ​

Answer 1

Answer:

(0,5)(0,-5)

Explanation:

Answer 2

The point on the curve x²/9 + y²/25 = 1 where tangent is parallel to x axis are (0,5) , (0, - 5)

Given : The equation of the curve x²/9 + y²/25 = 1

To find : The point on the curve where tangent is parallel to x axis

Solution :

Step 1 of 2 :

Find the slope of the curve

Here the given equation of the curve is

$\displaystyle \sf{ \frac{ {x}^{2} }{9} + \frac{ {y}^{2} }{25} = 1 } \: \: \: - - - - (1)$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{ 2x }{9} + \frac{ 2y }{25} \frac{dy}{dx} = 0 }$

$\displaystyle \sf{ \implies \frac{dy}{dx} = - \frac{25x}{9y} }$

Step 2 of 2 :

Find the required point

Since the tangent is parallel to x axis

Slope of the curve = 0

$\displaystyle \sf{ \implies \frac{dy}{dx} = 0}$

$\displaystyle \sf{ \implies - \frac{25x}{9y} = 0 }$

$\displaystyle \sf{ \implies x = 0 }$

From Equation 1 Putting x = 0 we get

$\displaystyle \sf{ \frac{ {y}^{2} }{25} = 1 }$

$\displaystyle \sf{ \implies {y}^{2} = 25 }$

$\displaystyle \sf{ \implies y = \pm \: 5}$

Hence the required points are (0,5) , (0, - 5)

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