For the origin O, given two points A and B such that `/_AOB=90^(@)` on a parabola `y=x^(2)` .The line joining A and B has slope 2.On the basis of above information,answer the following questions: The area of `Delta OAB` is -

For the origin O , given two points A and B such that /_AOB=90^(@) on a parabola y=x^(2) . The line joining A and B has slope 2. On the basis of above information, answer the following question: The equation of line AB is

For the origin O given two points A and B such that /_AOB=90^(@) on a parabola y=x^(2) .The line joining A and B has slope 2. on the basis of above information answer the following questions: The equation of line AB is

Consider a parabola y^(2)=4x. Image the focus of parabola in any tangent L.of parabola is the centre of a circle C which also touches the line L.On the basis of above information,answer the following questions.If radius of circle C is equal to latus rectum of given parabola,then slope of common tangent L.can be

In a DeltaABC with usual notations given that a = 4sqrt3, b=4 and c=4. If DEF is the triangle formed by joining the point of contact of the incirclewith the sides of the triangle ABC respectively, then (as shown in figure)On the basis of above information, answer the following questions :Jaradius of triangle ABC is equal to -

Two tangents are drawn from point P(h,0),h<0 to the circle x^(2)+y^(2)-4x=0 which touches the circleat A&B and rhombus PACB is then completed.On the basis of above information,answer the following questions: If point P be such that C lies on the circle,then h is equal to

Consider a triangle OAB on the xy- plane in which O is taken as origin of reference and position vector of A and B are vec aandvec b respectively. A line AC parallel to OB is drawn a from A. D is the mid point of OA. Now a line DC meets AB at M. Area of DeltaABC is 2 times the area of DeltaOAB On the basis of above information, answer the following questions 1. Position vector of point C is 2. Position vector of point M is

Parabola y^(2)=x+1 cuts the Y-axis in A and B. The sum of slopes of tangents to the parabola at A and B is