Let `P` be a point on the hyperbola `x^2-y^2=a^2,` where `a` is a parameter, such that `P` is nearest to the line `y=2xdot` Find the locus of `Pdot`

Find the point on the hyperbola x^2-9y^2=9 where the line 5x+12 y=9 touches it.

Find the nearest point on the line 2x+y=5 from the origin.

Find the nearest point on the line x - 2y=5 from the origin.

Find the point on 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.

The tangents to x^2+y^2=a^2 having inclinations alpha and beta intersect at Pdot If cotalpha+cotbeta=0 , then find the locus of Pdot

Find the nearest point on the line 2x + y = 5 from the origin.

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1 . If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

Find the nearest point on the line x - 2y- 5 from the origin.

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O PdotO Q=p^2 , then find the locus of the point Qdot