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The points on the curve x2/9 + y2/16 = 1 at which the tangents are parallel to y - axis are :(a) (0,±4)(b) (±4,0)(c) (±3,0)(d) (0, ±3) |
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Answer» Option : (c) \(\frac{x^2}{9}+\frac{y^2}{16}=1\;\Rightarrow\frac{2x}{9}+\frac{2y}{16}\frac{dy}{dx}=0\) \(\Rightarrow\) slope of normal \(=\frac{-dx}{dy}=\frac{9y}{16x}\) As curve’s tangent is parallel to y-axes Therefore, the normal to the curve is parallel to x-axis \(\Rightarrow\frac{9y}{16x}=0\Rightarrow y=0\;and\,x=\pm3\) \(\therefore\,points=(\pm3,0)\) |
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