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if a line 3x + 4y= -7 1/2 touches the ellipse 3x 2 +4y 2 =1 then the point of contact is,

if a line 3x + 4y= -71/2 touches the ellipse 3x2 +4y2 =1 then the point of contact is,

Grade:12

3 Answers

Vikas TU
14149 Points
2 years ago
Dear student 
3x + 4y= -7^1/2 is a line .......1
3x2 +4y2 =1 is ellipse .........2
Please confirm that it can not be -7^0.5 , It will become imaginary . 
Please post the image.
We will help you 
Good Luck 
 
Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
Dear student

Obtain equation of line in terms of one variable ie x = …

Or y = ...

Substitute it in second eqn

Solve the modified second eqn

Roots will be ( -(7)^(-0.5) , -(7)^(-0.5))

Which can otherwise be also guessed or verified

Regards

Aditya Gupta
2081 Points
2 years ago
let line touch ellipse at P(cosp/sqrt3, sinp/2).
eqn of ellipse at P would be 3xx1+4yy1= 1 or 3xcosp/sqrt3 + 4ysinp/2= 1
or sqrt3xcosp + 2ysinp= 1
given line 3x + 4y= -71/2 
since both must be identical, we have
sqrt3*cosp/3= 2sinp/4= 1/-71/2 
or cosp/sqrt3= sinp/2= 1/-71/2 
hence P(cosp/sqrt3, sinp/2)= ( – 1/71/2, – 1/71/2).

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