Area enclosed by the curve `y=f(x)` defined parametrically as `x=(1-t^ – InterviewSolution

InterviewSolution

1.	Area enclosed by the curve `y=f(x)` defined parametrically as `x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2))` is equal toA. `pi` sq. unitsB. `pi//2` sq. unitsC. `(3pi)/(4)` sq. unitsD. `(3pi)/(2)` sq. units
Answer» Correct Answer - A Clearly t can be any real number `"Let "t=tan theta rArr x=(1-tan^(2)theta)/(1+tan^(2)theta)` `rArr" "x=cos 2theta and y =(2 tan theta)/(1+tan^(2)theta)=sin 2theta` `rArr" "x^(2)+y^(2)=1` Thus, required area is `pi` sq. units.

Discussion

No Comment Found

Related InterviewSolutions

The area bounded by the graph of `y=f(x), f(x) gt0` on [0,a] and x-axis is `(a^(2))/(2)+(a)/(2) sin a +(pi)/(2) cos a ` then find the value of `f((pi)/(2))`.
If the area bounded by the x-axis, the curve `y=f(x), (f(x)gt0)" and the lines "x=1, x=b " is equal to "sqrt(b^(2)+1)-sqrt(2)" for all "bgt1,` then find f(x).
Find the continuous function `f`where `(x^4-4x^2)lt=f(x)lt=(2x^2-x^3)`such that the area bounded by `y=f(x),y=x^4-4x^2dot`then y-axis, and the line `x=t ,`where `(0lt=tlt=2)`is `k`times the area bounded by `y=f(x),y=2x^2-x^3,y-a xi s ,`and line `x=t(w h e r e0lt=tlt=2)dot`
In any ΔABC, D is a point on BC such that ar (ΔABD) = ar (ΔADC then \(\overline{AD}\) represents. A) Altitude B) Median C) Angle bisector D) Perpendicular Bisector
If 1 cm represents 2.5 m then area of a square with 10 m is A) 10 cm2B) 4 cm2 C) 2.5 cm2 D) 1 cm2
If 1 cm represents 5 in, what would be an area of 6 cm2 represents ?
Rajni says 1 sq. m = 1002 sq. cm. Do you agree ?
In the adjacent figure the ratio of ar (ΔAPB) and ar (ΔDQC) is ……………….A) 1 : 2 B) 2 : 1 C) 1 : 1 D) 1 : 3
The area of parallelogram ABCD is 36cm2 . Calculate the height of parallelogram ABEF if AB = 4.2 cm.
P is a point in the interior of a parallelogram ABCD. Show that ar (ΔAPB) + ar (ΔPCD) = 1/2 ar(ABCD) (Hint : Through P, draw a line parallel to AB)