A dog wants to catch a cat. The dog follows the path whose equation is y − 2 x = 0 while the cat follows the path whose equation is x 2 + y 2 = 20 . The coordinates of possible point(s) of catching th

Question

A dog wants to catch a cat. The dog follows the path whose equation is y − 2 x = 0 while the cat follows the path whose equation is x 2 + y 2 = 20 . The coordinates of possible point(s) of catching the cat is (are)

TestHub · Accepted Answer

A catch point must lie on both paths, so solve the two equations together.

Dog: $y = 2 x$

Cat: $x^{2} + y^{2} = 20$

Substitute: $x^{2} + 4 x^{2} = 20$

$5 x^{2} = 20 \Rightarrow x = \pm 2$

Since $y = 2 x$ , y takes the same sign as x: $y = \pm 4$

Possible catch points: (2, 4) and (-2, -4). Hence (A) and (D).

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