The condition that lx+my+c=0 maybe a normal to the parabola with related example
The condition that lx+my+c=0 maybe a normal to the parabola with related example
Jijo , 7 Years ago
Grade 12
Analytical Geometry> The condition that lx+my+c=0 maybe a norm...
1 Answers
Arun
the condition of the given parabola is y2=4ax
the condition of the ordinary to the given parabola is y+tx=2at+at3
i.e. tx+y−(2at+at3)=0 ........(1)
the condition (1) and the given condition of the ordinary lx+my+n=0 ...........(2) speak to a similar line:
subsequently
t/l=1/m=−(2at+at3)/n
t/l=1/m⇒t=l/m ........(3)
furthermore, 1/m=−(2at+at3)n
−n/m=2at+at3
−n/m=2a.(l/m)+a.(l/m)3 [ substituting the estimation of t from eq(3)]
−n/m=2a.l/m+a.(l/m)3
⇒−n.m2=2a.lm2+a.l3
⇒a.l3+2alm2+nm2=0
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
1 Answer Available
Last Activity: 3 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
1 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
1 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
1 Answer Available
Last Activity: 3 Years ago