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Grade: 12

                        

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,

one year ago

Answers : (3)

Vikas TU
14149 Points
							
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 
 
one year ago
Saurabh Koranglekar
askIITians Faculty
10341 Points
							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

one year ago
Aditya Gupta
2074 Points
							
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).
10 months ago
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