find the value of k in which straight line 3x+4y=k touches the circle x^2+y^2=10x
find the value of k in which straight line 3x+4y=k touches the circle x^2+y^2=10x
nishanth senthilvelan , 12 Years ago
Grade
Analytical Geometry> circle...
2 AnswersHimanshu Sharma
Last Activity: 12 Years ago
it''s quite simple
simply first put the eqn of line in the curve
3x+4y=k
(k-3x)/4=y
put this in the curve
x^2+(k-3x/4)^2=10x
16x^2+k^2+9x^2-6kx=160x
25x^2+x(-6k-160)+k^2=0
now this quadratic equation will have only one solution because this line touches it at only one point hence the value of x should come out only one.
so Discriminant of this eqn is 0(for same roots)
36k^2+25600+1920k-4*25*k^2=0
hence k=40,-10
Please rate if it helped
ankitesh gupta
Last Activity: 12 Years ago
PLZZZZZZZZZZZZZZZZZ APPROVE THE ANSWER IF YOU ARE SATISFIED BY CLIKING THE YES BUTTON ......................
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
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