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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
one year 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 10341 Points
one year 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
2075 Points
one year 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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