Home
Class 12
MATHS
If the line 3x+4y=sqrt7 touches the elli...

If the line `3x+4y=sqrt7` touches the ellipse `3x^(2)+4y^(2)=1`, then find the point of contact.

Text Solution

Verified by Experts

Equation of given tangent is
`3x+4y=sqrt(7)`
Let the line touch the given ellipse at point `P(x_(1),y_(1))" "(1)`
Thus, eqution of tangent toe ellipse at point P is
`3x x_(1)+4yy_(1)=1" "(2)`
Equation (1) an (2) represent the ame stright line.
`:. (3x_(1))/(3)=(4y_(1))/(4)=(1)/(sqrt7)`
`:. P(x_(1),y_(1))-=((1)/(sqrt7),(1)/(sqrt(7)))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

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

Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

Show that the line 3x+4y +20=0 touches the circle x^(2) + y^(2) =16 and find the point of contact

Prove that the straight line y = x + a sqrt(2) touches the circle x^(2) + y^(2) - a^(2)=0 Find the point of contact.

Show that the line y= x + sqrt(5/6 touches the ellipse 2x^2 + 3y^2 = 1 . Find the coordinates of the point of contact.

The line 2x-3y=9 touches the conics y^(2)=-8x . find the point of contact.

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

Show that the line x + ny + an ^(2) =0 touches the parabola y ^(2) = 4 ax and find the point of contact.

If x/a+y/b=sqrt(2) touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentric angle theta of point of contact.