1800-150-456-789
FlagBACK
Flag Analytical Geometry> Prove that the tangents from the points (...
question mark

Prove that the tangents from the points (1,2√2) , (2√2,1) , (2,√5), (√5,2) to the ellipse 5x2+4y2=1 are perpendicular.

supraja venkatraman , 6 Years ago
Grade 11
anser 2 Answers
Saurabh Koranglekar

Last Activity: 5 Years ago

576-1020_1.PNG

Vikas TU

Last Activity: 5 Years ago

16x^2−25y^2 =400
 
tangents from (2sqrt(2),1) is y=mx+c
 
c=1−2msqrt(2)
​
 
 
tangent to the hyperbola in slope form is 
 
y=mx± sqrt(a^2m^2 −b^2)
 
c=1−2msqrt2
​
square both side
 
1+8m^2−4sqrt2m=25m^2−16
17m^2+4sqrt(2)m−17=0
 
from above equation we will get slope of tangents m1,m2
​
but before solving this we can see that m1m2 =−1
 
it means tangents are perpendicular to each other.

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on analytical geometry

question mark
  • 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

question mark
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

question mark
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

question mark
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

question mark
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