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 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

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 ?

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.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 ?

If the slope of the line joining the points A(x,2) and B(6,-8) is find the value of x.

The line y=2x-k, k ne 0 , meets the parabola y=x^(2)-4x at points A and B. If angle AOB=pi//2 , then value of k is