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`

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=2x. Find the locus of P.

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=2x . Show that the locus of P is 2y-x=0 .

If P(x_(1),y_(1)) is a point on the hyperbola x^(2)-y^(2)=a^(2) , then SP.S'P= . . . .

Tangents are drawn from a point P to the hyperbola x^(2)-y^(2)=a^(2) If the chord of contact of these normal to the curve,prove that the locus of P is (1)/(x^(2))-(1)/(y^(2))=(4)/(a^(2))

P (2 , k) is on the ellipse x^(2) + 2y^(2) = 6 . For what value of k the point P is nearest to the line x + y = 7 ?

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

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

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

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

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