Let two sides of a rectangle of area 20 sq. units are along lines x – y = 0 and x + y = 2 , then the locus of the point of intersection of diagonals is a

Question

Let two sides of a rectangle of area 20 sq. units are along lines x – y = 0 and x + y = 2 , then the locus of the point of intersection of diagonals is a, pair of ellipse, pair of straight lines, pair of hyperbola having eccentricity 2 and 2 3, pair of hyperbola each having eccentricity 2

MARKS App · Accepted Answer

Let diagonals A C & B D intersect at F h , k ⇒ Area of quad D E F G is 1 4 20 = 5 Now distance of h , k from x + y = 2 and x – y = 0 is h + k - 2 2 & h - k 2 respectively. ⇒ h + k - 2 2 h - k 2 = 5 ⇒ ( h - 1 ) + ( k - 1 ) h - 1 - k - 1 = 10 ⇒ ( h - 1 ) 2 - ( k - 1 ) 2 = 10 ⇒ ( x - 1 ) 2 - ( y - 1 ) 2 = 10 or x - 1 2 - y - 1 2 = - 10 ⇒ Both are hyperbola with eccentricity = 2

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