Let $$A(0$$,$$0)$$, $$B(5$$,$$0)$$, $$C(5$$,$$3)$$ and $$D(0$$,$$3)$$ be the vertices of rectangle ABCD, If P is a variable point lying inside the rectangle ABCD and d (P$$, $$L) denotes perpendicular distance of point P from line LIf $$d(P$$,$$AB)$$≤$$min{d(P$$,$$BC)$$,$$d(P$$,$$CD)$$,$$d(P$$,$$AD)}$$ then area of the region in which P lies is (in$$ sq.$$units)If$$ $$d(P$$,$$AB)≥$$maxd(P$$,$$BC)$$,$$d(P$$,$$CD)$$,$$d(P$$,$$AD)$$ then the area of the region in which P lies is (in$$ sq.$$units)If$$ $$d(P$$,$$AB)−$$322+(d(P$$,$$AD))2$$≥$$1$$, then area of region in which P lies is (in$$ sq.$$units)

Question

Let $$A(0$$,$$0)$$, $$B(5$$,$$0)$$, $$C(5$$,$$3)$$ and $$D(0$$,$$3)$$ be the vertices of rectangle ABCD, If P is a variable point lying inside the rectangle ABCD and d (P$$, $$L) denotes perpendicular distance of point P from line LIf $$d(P$$,$$AB)$$≤$$min{d(P$$,$$BC)$$,$$d(P$$,$$CD)$$,$$d(P$$,$$AD)}$$ then area of the region in which P lies is (in$$ sq.$$units)If$$ $$d(P$$,$$AB)≥$$maxd(P$$,$$BC)$$,$$d(P$$,$$CD)$$,$$d(P$$,$$AD)$$ then the area of the region in which P lies is (in$$ sq.$$units)If$$ $$d(P$$,$$AB)−$$322+(d(P$$,$$AD))2$$≥$$1$$, then area of region in which P lies is (in$$ sq.$$units)

Infinity Learn · Accepted Answer

$$d(P$$,$$AB)$$≤$$d(P$$,$$BC)d(P$$,$$AB)$$≤$$d(P$$,$$CD)d(P$$,$$AB)$$≤$$d(P$$,$$AD)$$⇒P lies in region as $$shownArea=12$$×$$32$$×$$7=214d(P$$,$$AB)$$≥$$d(P$$,$$BC)d(P$$,$$AB)$$≥$$d(P$$,$$CD)d(P$$,$$AB)$$≥$$d(P$$,$$AD)$$⇒P lies in region as $$shownArea==12$$×$$1$$×$$12=14x2+y$$−$$322$$≥$$1P$$ lies in region as shownArea $$=5$$×$$3$$−π$$(1)22=15$$−π$$2$$

Detailed Solution

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