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Find the points on the curve (x^2)/4+...

Find the points on the curve `(x^2)/4+(y^2)/(25)=1` at which the tangents are parallel to the x-axis and y-axis.

Text Solution

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Equation of the curve is,
`x^2/4+y^2/25 = 1->(1)`
(i) When tangents are parallel to x-axis,
`dy/dx = 0`
Differentiating (1) w.r.t. `x`,
`=>1/4(2x)+1/25(2y)dy/dx = 0`
`=>dy/dx = -x/4(25/y) = (-25x)/(4y)`
As, `dy/dx = 0 =>(-25x)/(4y) = 0 => x = 0`
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