TS EAMCET · Maths · Straight Lines
A point moves in the \(x y\)-plane such that the sum of its distance from two mutually perpendicular lines is always equal to 5 units. The area (in sq units) enclosed by the locus of the point, is
- A \(\frac{25}{4}\)
- B \(25\)
- C \(50\)
- D \(100\)
Answer & Solution
Correct Answer
(C) \(50\)
Step-by-step Solution
Detailed explanation
In a figure, \(x x^{\prime}\) and \(y y^{\prime}\) are two perpendicular axes. \(\therefore \quad|x|+|y|=5\) \(\therefore\) Coordinates of \(B\) and \(C\) are \((5,0)\) and \((0,5)\). \(\therefore\) Length of \(B C=\sqrt{5^2+5^2}=5 \sqrt{2}\) \(\therefore\) Area of square…
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