The tangent at any point of a circle is perpendicular to the radius through the point of contact.

A tangent is perpendicular to the radius at the

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________

The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is__________

Choose the correct answer and give justification for each. (i) The angle between a tangent to a circle and the radius at the point of contact is

The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of the curve through the point (1,1) is

Fill in the blanks A tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q so that OQ=13cm . Find length of PQ.

Tangent to a curve intercepts the y-axis at a point P A line perpendicular to this tangent through P passes through another point (1,0). The differential equation of the curve is

The tangents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B, the other end of the diameter, through, A. The sum of focal distance of any point on the curce is

Three circles touch each other externally. The tangents at their point of contact meet at a point whose distance from a point of contact is 4. Then, the ratio of their product of radii to the sum of the radii is