Geometry

Miscellaneous

Medium

The point (x, y) is equidistant from the points (2, 4) and (1, 8). Find the relation between x and y.

2x – 8y = –45

4x + 3y = –35

7x – 3y = 45

x – 5y = 35

✅ Correct Option: 1

Equating squared distances, $(x-2)^2 + (y-4)^2 = (x-1)^2 + (y-8)^2$ . Expanding gives $-4x + 20 - 8y = -2x + 65 - 16y$ , so $-2x + 8y = 45$ , that is $2x - 8y = -45$ .

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LIST-I (Geometrical Function)		LIST-II (Formula)
A. Area of a Triangle	I.	2 (Length + Breadth)
B. Perimeter of a Rectangle	II.	$\pi\times(\text{Radius})^2$
C. Area of a Parallelogram	III.	1/2 ( Base × Height)
D. Area of a Circle	IV.	Base × Height

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The point (x, y) is equidistant from the points (2, 4) and (1, 8). Find the relation between x and y.

Solution

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