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Focii of Hyperbola

State whether...

Question

State whether the following statement is true or false.
The point P (2, 4) lies on a circle of radius 6 and centre C (3, 5).
Enter $1$ for true and $0$ for false.

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Solution

$T h e g i v e n p o i n t P (x_{1}, y_{1}) = (2, 4) w i l l l i e o n t h e c i r c l e w i t h c e n t r e a t$

$C (x_{2}, y_{2}) = (3, 5) a n d r a d i u s r = 6 . u n i t s i f a n d o n l y i f r = P C .$

$N o w P C = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(2 - 3)}^{2} + {(4 - 5)}^{2}} u n i t s = \sqrt{2} u n i t s .$

$B u t g i v e n t h a t r = 6 u n i t s .$

$∴ P C \neq r a n d P C < r .$

$S o P d o e s n o t l i e o n t h e c i r c l e . R a t h e r, P l i e s w i t h i n t h e c i r c l e .$

$A n s - F A L S E .$

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