Question

The point $(1,4)$ lies inside the circle $x^2+y^2-6x-10y+p=0$ which does not touch or intersect the coordinate axes, the

• A. $0<p<29$
• B. $25<p<29$
• C. $9<p<25$
• D. $9<p<29$

Answer 1

Answer: (B)

$25<p<29$

Since the circle does not touch or intersect the coordinates axes, the absolute values of $x$ and $y$ coordi-nates of the greater than the radius of the circle.

Coordinates of the centre of the circle are $(3,5)$ and the radius is $\sqrt{9+25-p}$

so that $3>\sqrt{9+25-p}\Rightarrow p>25$ ...(1)

$5>\sqrt{9+25-p}\Rightarrow p>9$ ...(2)

and the point $(1,4)$ lies inside the circle

$\Rightarrow 1+16-6-10\times 4+p<0\Rightarrow p<29$ ..(3)

From (1), (2), (3) we get $25<p<29$