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Prove that line y= x+√7/12 is the tangent of ellipse 3x^2 +4y^2= 1.

Prove that line y= x+√7/12 is the tangent of ellipse 3x^2 +4y^2= 1.

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
for provng tangency we have to prove
c2 = a2* m2 + b2
 
Now
ellipse:
x^2 / (1/3) + y^2 / (1/4)   = 1
a2 =1/3
b2 = ¼
 
now RHS
a2* m2 + b2
 = 1/3 * 1 + ¼
 = 1/3 + ¼
 = 7/12
 = c2
 = LHS
Hence proved
It will be a tanget to the given ellipse
 
Regards
Arun (askIITians forum expert)

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