Tangents are drawn from the origin to curve `y=sinxdot` Prove that points of contact lie on `y^2=(x^2)/(1+x^2)`

Tangents are drawn from origin to the curve y = sin+cos x ·Then their points of contact lie on the curve

Tangents are drawn from the points on the line x-y-5=0 to x^(2)+4y^(2)=4 . Prove that all the chords of contact pass through a fixed point

Tangents are drawn from the points on the line x-y-5=0 to x^2+4y^2=4 . Then all the chords of contact pass through a fixed point. Find the coordinates.

Tangent are drawn from the point (3, 2) to the ellipse x^2+4y^2=9 . Find the equation to their chord of contact and the middle point of this chord of contact.

Tangent is drawn at any point (x_1, y_1) other than the vertex on the parabola y^2=4a x . If tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass through a fixed point (x_2,y_2), then (a) x_1,a ,x_2 in GP (b) (y_1)/2,a ,y_2 are in GP (c) -4,(y_1)/(y_2), (x_1//x_2) are in GP (d) x_1x_2+y_1y_2=a^2

Let 2 x^2 + y^2 - 3xy = 0 be the equation of pair of tangents drawn from the origin to a circle of radius 3, with center in the first quadrant. If A is the point of contact. Find OA

A pair of tangents are drawn from the origin to the circle x^2+y^2+20(x+y)+20=0 . Then find its equations.

From the point (2, 2) tangent are drawn to the hyperbola (x^2)/(16)-(y^2)/9=1. Then the point of contact lies in the (a)first quadrant (b) second quadrant (c)third quadrant (d) fourth quadrant

Tangents are drawn from the point P(3, 4) to the ellipse x^2/9+y^2/4=1 touching the ellipse at points A and B.

A pair of tangents are drawn from the origin to the circle x^2 + y^2 + 20x +20y + 20 = 0 , The equation of pair of tangent is