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Grade 12Analytical Geometry

If P (2,8) is an interior of a circle x² + y² + 4y – p = 0 which neither touches nor intersects the axes, then set for p is -

(a) p < - 1

(b) P < - 4

(c) p > 96

(d) f

Rakesh Singh

12 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:

Equation of circle:

$x^{2}+(y+2)^{2} = (\sqrt{p+4})^{2}$

$p+4> 0$

$\Rightarrow p> -4$ ...........(1)

P(2, 8) is interior to the circle

$2^{2}+8^{2}+4.8-p< 0$

$\Rightarrow p> 100$

If there is no condition on touching or intersexting the x- axis, then

$\Rightarrow p> 100$

If circle is not touching & intersecting the x-axis, we have

$0< \sqrt{p+4}< 2$

$-4< p< 0$

Thanks & Regards

Jitender Singh

IIT Delhi

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