QJEEM10Madd05: JEE Main 2010 Mathematics - Class 11 JEEM10Madd05 Solution: The circle x 2 + y 2 = 4 x + 8 y + 5 intersects the line 3 x −…

Question

Verified Solution • 2025–26 Session moderate

The circle

x^{2} + y^{2} = 4 x + 8 y + 5

intersects the line

3 x - 4 y = m

at two distinct points if :

Accepted Answer

Circle

x^{2} + y^{2} - 4 x - 8 y - 5 = 0

Center

= (2, 4),

Radius

= \sqrt{4 + 16 + 5} = 5

If circle is intersecting line

3 x - 4 y = m,

at two distinct points.

\Rightarrow

length of perpendicular from center to the line

<

radius

\Rightarrow \frac{| 6 - 16 - m |}{5} < 5 \Rightarrow | 10 + m | < 25

\Rightarrow - 25 < m + 10 < 25 \Rightarrow - 35 < m < 15

Step-by-Step Verified Solution