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`.

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.

A point on the hyperbola x^(2)-3y^(2)=9, where the tangent is parallel to the line y+x=0, is

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))

Let (x,y) be any point on the parabola y^(2)=4x. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let p ( h,k) be a point on the curce y = x^2 + 7x + 2 , nearest to the line y = 3x -3 . then the equation of the normal to the curve at P is :

Let (x, y) be any point on the parabola y^(2) = 4x . Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is

If P be a point on the lane lx+my+nz=p and Q be a point on the OP such that OP. OQ=p^2 show that the locus of the point Q is p(lx+my+nz)=x^2+y^2+z^2 .