A tangent to a curve at P(x, y) intersects x-axis and y-axis at A and B respectively. Let the point of contact divides AB in the ratio `y^2 : x^2`.

Draw the graph of x+y=6 which intersects the X-axis and Y-axis at A and B respectively. On the same graph paper, draw the graph of 2x-y=3 which intersects the X-axis and Y-axis at C and D respectively. E is the point of intersection of both the graphs. Find the areas of /_\ ECA /_\ EBD.

If the tangent to the curve x = at^2 , y = 2at is perpendicular to x-axis then what is its point of contact ?

The straight line 4x + 3y - 12 = 0 intersects the x -and y-axis A and B respectively. Find the coordinates of the point at which the straight line bar(AB) is divided internally into the ratio 2 : 1.

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the equation of line AB.

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the slope of line AB

Let y=f(x) be a curve passing through (4,3) such that slope of normal at any point lying in the first quadrant is negative and the normal and tangent at any point P cuts the Y-axis at A and B respectively such that the mid-point of AB is origin, then the number of solutions of y=f(x) and y=|5-|x||, is

If a variable tangent to the curve x^(2)y=c^(3) make intercepts a,b on x and y axis respectively.Then the value of a^(2)b is

Consider the circle x^2+y^2=9 and the parabola y^2=8x . They intersect at P and Q in the first and fourth quadrants, respectively. Tangents to the circle at P and Q intersect the X-axis at R and tangents to the parabola at P and Q intersect the X-axis at S. The ratio of the areas of trianglePQS" and "trianglePQR is