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

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.

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
11 months ago
576-1020_1.PNG
Vikas TU
14148 Points
11 months 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.

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