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

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 -

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

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

A consumer has total money income of Rs.500 to be spent on two goods x and y with prices of Rs.50 and Rs.10 per unit respectively. On the basis of the given information, answer the following question : (a)Give the equation of the budget line for consumer. (b)What is the value of slope of the budget line ? (c )How many units can the consumer buy if he is to spend all his money income on good x ? (d) How does the budget line change if there is a 50% falls in price of good y ?

A consumer has total money income of Rs.250 to be spent on two goods X and Y with prices of Rs.25 and Rs.10 per unit respectively.On the basis of the given information , answer the following questions : (a) Given the equation of the budget line for the consumer. (b)What is the value of slope of the budget line ? (c )How many units can the consumer buy if he is to spend all his money income on good X ? (d)How does the budget line change if there is a fall in price of good Y ?

A point (-4,1) divides the line joining A(2,-2) and B(x,y) in the ratio 3:5. Then point B is

If the line 5x-4y-12=0 meets the parabola x^(2)-8y in A and B then the point of intersection of the two tangents at A and B is