CircleHard
Question
The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x - 4y = m at two distinct points if
Options
A.-35 < m < 15
B.15 < m < 65
C.35 < m < 85
D.-85 < m < -35
Solution
Circle x2 + y2 - 4x - 8y - 5 = 0
Centre = (2, 4), Radius =
= 5
If circle is intersecting line 3x - 4y = m
at two distinct points.
⇒ length of perpendicular from centre < radius
⇒
⇒ |10 + m| < 25
⇒ -25 < m + 10 < 25
⇒ -35 < m < 15.
Centre = (2, 4), Radius =
= 5If circle is intersecting line 3x - 4y = m
at two distinct points.
⇒ length of perpendicular from centre < radius
⇒
⇒ |10 + m| < 25
⇒ -25 < m + 10 < 25
⇒ -35 < m < 15.
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