Question
The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is(A) $(2 \sqrt{2}, 4)$(B) $(2 \sqrt{2}, 0)$(C) $(0,0)$(D) $(2,2)$
Step 1
Step 1: The distance between any point $(x, y)$ on the curve $x^{2}=2 y$ and the point $(0,5)$ is given by \[d=\sqrt{(x-0)^{2}+(y-5)^{2}}=\sqrt{x^{2}+(y-5)^{2}}\] Show more…
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The point $(0,5)$ is closest to the curve $x^{2}=2 y$ is (a) $(2 \sqrt{2}, 0)$ (b) $(0,0)$ (c) $(2,2)$ (d) None
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The points on the curve $5 x^{2}-6 x y+5 y^{2}=4$ that are the nearest the origin are (a) $(1 / 2,-1 / 2),(-1 / 2,1 / 2)$ (b) $(0,2 / \sqrt{5}),(0,-2 / \sqrt{5})$ (c) $(2 \sqrt{5}, 0),(-2 / \sqrt{5}, 0)$ (d) $(2 / \sqrt{3}, 0),\left(\frac{2}{\sqrt{5}}, 1\right)$
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