Home
Class 11
MATHS
The line 2x+3y=12 touches the ellipse (x...

The line 2x+3y=12 touches the ellipse `(x^(2))/9+(y^(2))/4=2` at the points (3,2).

Text Solution

Verified by Experts

True
Given equation of line is
2x+3y =12…(i)
and ellipse`(x^(2))/9+(y^(2))/4=2`….(ii)
Since, the equation of tangent at (`x_(1),y_(1)`) is `("xx"_(1))/9+(yy_(1))/4=2`
`therefore` Tangent at (3,2).
`(3x)/9+(2y)/4=2`
`rArr x/3+y/2=2`
`rArr 2x+3y=12` which is given line.
Hence, the statement is true.
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Fillers|6 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Objective type|13 Videos

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Long answer|10 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Fillers|16 Videos

Similar Questions

Explore conceptually related problems

If the line y=x+sqrt(3) touches the ellipse (x^(2))/(4)+(y^(2))/(1)=1 then the point of contact is

Line 3x + 4y = 25 touches the circle x^(2) + y^(2) = 25 at the point

A line parallel to the line x-3y=2 touches the circle x^(2)+y^(2)-4x+2y-5=0 at the point

The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k is

If the line y=x+c touches the ellipse 2x^(2)+3y^(2)=1 then c=

The line y=2t^2 meets the ellipse (x^2)/(9)+(y^2)/(4)=1 in real points if

If the line 3x+4y=sqrt(7) touches the ellipse 3x^(2)+4y^(2)=1, then the point of contact is