AP EAMCET Engineering 18 Sep 2020 Shift 2 Paper

Section: Mathematics

Question : 40 of 160

Marks: +1, -0

The circle x2+y2−6x−10y+p=0 neither intersects nor touch the coordinate axes and the point (1,4) lies inside the circle.Then the range of possible values of ‘p’ is

$ 23
$ 25
$ 21
$ 12

Validate

Solution:

The equation of given circle is
x2+y2−6x−10y+p=0
⇒‌‌(x−3)2+(y−5)2=34−p
∴ The point (1,4) lies inside the circle, so
1+16−6−40+p<0
⇒‌‌p<29.........(i)
∴ The circle neither intersects nor touches the coordinate axis, then
r=√34−p<3⇒34−p<9
⇒‌‌p>25 ...(ii)
and ‌‌r=√34−p<5
⇒‌‌34−p<25
⇒‌‌p>9.....(iii)
from in equalities Eqs. (i), (ii) and (iii), we get
$25

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