Given is a polar `4x + y +12 =0` of the parabola `y^2 = -4x`; find coordinates of the pole and write equations of the corresponding tangents.

The line x+14y=25 is the polar of the ellipse x^(2)+4y^(2)=25. Find coordinates of the pole.

Tangents PT and QT to the parabola y^2 = 4x intersect at T and the normal drawn at the point P and Q intersect at the point R(9, 6) on the parabola. Find the coordinates of the point T . Show that the equation to the circle circumscribing the quadrilateral PTQR , is (x-2) (x-9) + (y+3) (y-6) = 0 .

The equation of the directrix of a parabola is x = y and the coordinates of its focus ar (4,0) . Find the equation of the parabola.

Find the coordinates of the points at which the circles x^2+y^2-4x-2y=4 and x^2+y^2-12x-8y=12 touch each other. Find the coordinates of the point of contact and equation of the common tangent at the point of contact.

The line y = 2x-12 is a normal to the parabola y^(2) = 4x at the point P whose coordinates are

The equation of the tangent to the parabola y^(2) = 4x at the point t is

The equation of tangent in slope form to the the parabola y^2 = 4x is

The pole of the line 2x+3y-4 =0 with respect to the parabola y^(2)=4x is

Tangent are drawn from the point (-1,2) on the parabola y^2=4x . Find the length that these tangents will intercept on the line x=2.