Circle x^2 + y^2 - 4x - 8y - 5 = 0 will intersect the line 3x - 4… - Vidyadip

MCQ

Circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$ will intersect the line $3x - 4y = m$ in two distinct points, if

A
$ - 10 < m < 5$
B
$9 < m < 20$
✓
$ - 35 < m < 15$
D
None of these

✓

Answer

Correct option: C.

$ - 35 < m < 15$

c
(c) Radius of given circle > Perpendicular distance from the centre of circle to the given line.

$ \Rightarrow \sqrt {4 + 16 + 5} > \frac{{3(2) - 4(4) - m}}{{\sqrt {9 + 16} }}$

$ \Rightarrow \pm 25 > - 10 - m $

$\Rightarrow m + 10 > \pm 25$

$ \Rightarrow - 35 < m < 15$.

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