First slide

Definition of a circle

Question

If the point (3,4) lies inside and the point (-3,-4) lies outside the circle x²+y²-7x+ 5y -p =0. then the set of all possible values of p is

Easy

A

(24, 25)
B

(25, 26)
C

(24, 26)
D

(0, 24)

Solution

(3, 4) lies inside the circle
$\Rightarrow (3)^{2} + (4)^{2} - 7 (3) + 5 (4) - p < 0 \Rightarrow 24 < p$
(-3,-4) lies outside the circle
$\Rightarrow (- 3)^{2} + (- 4)^{2} - 7 (- 3) + 5 (- 4) - p > 0$
$\Rightarrow$ p< 26.
so, $p \in (24, 26)$

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