A tangent drawn to the curve `y=f(x)` at `P(x,y)` cuts the x-axis and y-axis at `A` and `B` respectively such that `BP:AP=2:1`. Given that `f(1)=1`. Answer the question:Equation of curve is (A) `y=1/x` (B) `y=1/x^2` (C) `y=1/x^3` (D) none of these

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:Equation of normal to curve at (1,1) is (A) x-4y+3=0 (B) x-3y+2=0 (C) x-2y+1=0 (D) none of these

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:The curve passes through the point (A) (2,1/4) (B) (2,1/2) (C) (2,1/8) (D) none of these

A tangent drawn to the curve y = f(x) at P(x, y) cuts the x and y axes at A and B, respectively, such that AP : PB = 1 : 3. If f(1) = 1 then the curve passes through (k,(1)/(8)) where k is

Tangent is drawn at any point P of a curve which passes through (1, 1) cutting x-axis and y-axis at A and B respectively. If AP: BP = 3:1 , then,

Area common to the curves y=sqrt(x) and x=sqrt(y) is (A) 1 (B) 2/3 (C) 1/3 (D) none of these

A curve y=f(x) passes through (1,1) and tangent at P(x , y) cuts the x-axis and y-axis at A and B , respectively, such that B P : A P=3, then (a) equation of curve is x y^(prime)-3y=0 (b) normal at (1,1) is x+3y=4 (c) curve passes through 2, 1/8 (d) equation of curve is x y^(prime)+3y=0

The area of the curve x + |y| = 1 and the y-axis is

The tangent to the curve x^(2) = 2y at the point (1,(1)/(2)) makes with the x-axis an angle of

At what points on the curve y=12(x+1)(x-2) is the tangent parallel to x-axis on [-1,\ 2] .

The area bounded by the curve y = (x - 1)^(2) , y = (x + 1)^(2) and the x -axis is