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 the origin to the curve y = sin x . Prove that their points of contact lie on the curve x^2y^2=(x^2-y^2) .

From the points on the circle x^(2)+y^(2)=a^(2) , tangents are drawn to the hyperbola x^(2)-y^(2)=a^(2) : prove that the locus of the middle-points (x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))

Let 2x^2 + y^2- 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.

Let 2x^(2)+y^(2)-3xy=0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the firs quadrant. If A is one of the points of contact, find the length of OA.

Tangents drawn from the point (4, 3) to the circle x^2+y^2-2x-4y=0 are inclined at an angle :

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

Find the slope of the tangent to curve y = x^3-x+1 at the point whose x-coordinate is 2.

The angle between the tangents drawn from origin to the parabola y^2= 12x from the point (-3,2) is :

Statement I Tangent drawn at the point (0, 1) to the curve y=x^(3)-3x+1 meets the curve thrice at one point only. statement II Tangent drawn at the point (1, -1) to the curve y=x^(3)-3x+1 meets the curve at one point only.

y=3x is tangent to the parabola 2y=ax^2+ab . If b=36,then the point of contact is