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A tangent to the hyperbola 3x^2 – 4y^2 = 12 makes equal intercept on the axes. Then the area of the triangle formed by the tangent with coordinate axes is ???? a)2 b)1/4 c)4 d)1/2 please give a complete solution for the question

A tangent to the hyperbola 3x^2 – 4y^2 = 12 makes equal intercept on the axes. Then the area of the triangle formed by the tangent with coordinate axes is ????
a)2
b)1/4
c)4
d)1/2
please give a complete solution for the question

Grade:12

2 Answers

Arun
25750 Points
4 years ago
x²/ 4 - y²/3 = 1 ⇒a² = 4, b² = 3
x/k + y/k = 1 or x + y = k or y = - x + k
⇒  m = -1 and c = k
Now k² = a² m² - b² 
= 4(-1)² - 3 
= 4-3 
= 1
⇒ k = + - 1
So the equation of the tangents are: x + y = + - or x + y + - = 0
it can also be taken as  x - y = k
Then k  = + - 1 and  x - y = + - 1
or x - y +-1 = 0
 
 
hence area = ½ * 1 * 1 = ½
 
ishu
13 Points
2 years ago
72 +82 hhhhh
bbbbbh
jjjj​   ∫87 \lim_{h\rightarrow 0} idk i’m writing all 
this for fun
\lim_{h\rightarrow \infty } x2 + y2 /8
87+98=67
hence ans is 89
= 4(-1)² - 3 
= 4-3 
= 1
⇒ k = + - 1
 

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