Question

Find the point which cut the line in 3 parts coordinate

Answer 1

Example: Find the points where the line 3x+y−5=0 cuts the given circle x2+y2=25. Also the length of the chord cut off form line by circle.

 

We have the given line and the circle

3x+y−5=0 - - - (i)x2+y2=25 - - - (ii)

First we find the points of intersection of the line (i) and the given circle (ii) by using the method of solving simultaneous equations, and from the line (i) we take the variable y separate as follows:

y=5−3x - - - (iii)

By putting the value of y from (iii) in equation (ii) we get these results:

x2+(5−3x)2=25⇒x2+25−30x+9x2=25⇒10x2−30x=0⇒10x(x−3)=0⇒x=0,x−3=0⇒x=0,x=3

By putting x=0 in equation (iii), we have y=5. This shows that one point of the intersection of the line and circle is A(0,5). Next, by putting x=3 in equation (iii) again we have y=−4. This shows that the other point of intersection of the line and circle is B(3,−4).

 

The length of the chord cut off from the line and the circle is given as using distance formula applying on these two points

|AB|=(0−3)2+(5−(−4))2−−−−−−−−−−−−−−−−−√=(−3)2+(9)2−−−−−−−−−−√=9+81−−−−−√=90−−√=9×10−−−−−√=310−−√

Line Touching Circle at One Point

Equations of Tangent and Normal to the Circle ⇒