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Last updated at April 19, 2021 by Teachoo

Example 17 Find points on the curve π₯^2/4 + π¦^2/25 = 1 at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.Given curve π₯^2/4 + π¦^2/25 = 1 Slope of the tangent is ππ¦/ππ₯ Finding π π/π π 2π₯/4+(2π¦ )/25 Γ ππ¦/ππ₯= 0 π₯/2 + 2π¦/25 ππ¦/ππ₯ = 0 2π¦/25 ππ¦/ππ₯ = (βπ₯)/2 ππ¦/ππ₯ = (βπ₯)/2 Γ 25/2π¦ π π/π π = (βπππ)/ππ Hence, ππ¦/ππ₯ = β (β25π₯)/4π¦ (i) Tangent is parallel to x-axis If the tangent is parallel to x-axis, its slope is 0 Hence, ππ¦/ππ₯ = 0 (β25π₯)/4π¦ = 0 x = 0 Putting x = 0 in equation of the curve π₯^2/4 + π¦^2/25 = 1 0/4 + π¦^2/25 = 1 π¦^2 = 25 y = Β± 5 Hence, the points are (0, 5) and (0, β5) (ii) Tangent is parallel to y-axis If the tangent is parallel to y-axis, its slope is 1/0 Hence, ππ¦/ππ₯ = 1/0 (β25π₯)/4π¦ = 1/0 y = 0 Putting y = 0 in equation of the curve π₯^2/4 + π¦^2/25 = 1 π₯^2/4 + 0/25 = 1 π₯^2/4 = 1 x2 = 4 x = Β± 2 Hence, the points are (2, 0) and (β2, 0)