IPMAT Question Paper 2019 | IPM Indore Quants

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Question 35: Two points on a ground are 1 m apart. If a cow moves in the field in such a way that it's distance from the two points is always in ratio 3: 2 then

1. the cow moves in a straight line
2. the cow moves in a circle
3. the cow moves in a parabola
4. the cow moves in a hyperbola

Video Explanation

Explanatory Answer

Let us say that the cow moves between the points O and A which are 1m apart.

For convenience, Let us fix O at (0,0) and A at (1,0).
Let us assume that B is at some point (x,y) where the cow is grazing. Let P be the perpendicular dropped from B on OA.



So OP = x and PA = 1-x

OB²= OP²+ BP²= x²+ y²
OB =\\sqrt{x^{2} + y^{2}}\\)
BA²= AP²+ BP²
BA²= (1-x)²+ y²
BA = \\sqrt{(1-x)^{2} + y^{2}}\\)

Also, \\frac{OB}{BA}\\) = \\frac{3}{2}\\)

\\frac{\sqrt{x^{2} + y^{2}}}{\sqrt{(1-x)^{2} + y^{2}}}\\) = \\frac{3}{2}\\)

\\frac{x^{2} + y^{2}}{(1-x)^{2} + y^{2}}\\) = \\frac{9}{4}\\)

4(x²+ y²) = 9((1−x)²+ y²) = 9 (1 + x²– 2x + y²)

4 x²+ 4 y²= 9 + 9 x²– 18x + 9y²
5x2 + 5y2 – 18x +9 = 0, This is an equation of locus of a Circle.

Hence, the cow moves in a Circular path.

The question is"Two points on a ground are 1 m apart. If a cow moves in the field in such a way that it's distance from the two points is always in ratio 3: 2 then"

Hence, the answer is the cow moves in a circle

Choice B is the correct answer

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