Find the point of the hyperbola (x^(2))/...

Find the point of the hyperbola `(x^(2))/(24)-(y^(2))/(18)=1` which is nearest to the line 3x+2y+1=0 and compute the distance between the point and the line.

Verified by Experts

The correct Answer is:

`(-6,3)` and `(11)/(sqrt(13))`units

Similar Questions

Explore conceptually related problems

The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 which is nearest to the line 3x+2y+1=0 are

Find the distance between the point (2,-1) and the line 4x-y=5

Find the distance between the point (1,-1) and the line 2x+y+3=0

Find the equation of tangnets to the hyperbola (x^(2))/(25)-(y^(2))/(36)=1 , parallel to the line 3x-3y=0

Find the points on the hyperbola 2x^(2)-3y^(2)=6 at which the slop of the tangent line is (-1)

Find the point of the circle x^(2)+y^(2)-6x+4y=0 which is (i) nearest (ii) farthest to the line 2x-3y+14=0 .

The point on the parabola y^(2)=64x which is nearest to the line 4x+3y+35=0 has coordinates

Find the points on the ellipse (x^2)/4+(y^2)/9=1 on which the normals are parallel to the line 2x-y=1.

The point on the parabola y^(2)=64x which is nearest to the line 4x+3y+35=0 has coordinates-

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.