Find the mid point of the chord 3x-y-1=0 to the circle x2+y2-4x+6y+1=0
Find the mid point of the chord 3x-y-1=0 to the circle x2+y2-4x+6y+1=0
HIMADRI BISWAS , 6 Years ago
Grade 11
Analytical Geometry> Find the mid point of the chord 3x-y-1=0 ...
1 Answers
kkbisht
Last Activity: 6 Years ago
The circle x2 + y2 -4x+6y+1=0 and the chord 3x-y-1=0 intersect at points given by x2 +(3x-1)2 -4x +6(3x-1) +1=0
=> x2 +9x2 +1 -6x -4x + 18x -6 +1=0 =>10x2 +8x-4=0 => 5x2 + 4x-2=0 => x= {-4 +-
16-4.5.(-2)}/10
x={-2+-214}/5
There fore y=3(-2+-214)/5) -1= ( -6+-614 +-5)/5 = (-11 +-614)/5
hence the mid point is x= ( x1+x2)/2={(-11 +214)/5 + (-11-214)/5}/2=-2/5
y= (y1 + y2)/2 =(-22/5)/2=-11/5
So mid point is : x=-2/5 , y=-11/5
K.K.Bisht
Provide a better Answer & Earn Cool Goodies
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Other Related Questions on analytical geometry
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
- The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is
analytical geometry
0 Answer Available
Last Activity: 2 Years ago
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)
analytical geometry
0 Answer Available
Last Activity: 3 Years ago
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0
analytical geometry
0 Answer Available
Last Activity: 3 Years ago
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.
analytical geometry
0 Answer Available
Last Activity: 3 Years ago
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d
analytical geometry
0 Answer Available
Last Activity: 3 Years ago