y2 = 4x
The area of the square bounded by x=0, x=4, y=4 and y=0 will be 4×4=16 square units.
Let f: y2=4x and g: x2=4y
Let I1 be the area bounded by the curve f and y-axis and I2 be the area bounded by the curve g and x-axis and I3 be the area bound in between f and g-curve.
Then, I1+I2+I3=16 –(1)
Substituting values of (2) and (3) in (1), we get
Hence, and therefore it divides the square in 3 equal parts.
The area of the triangle will be equal to
∆ABC= (area under line segment AB) + (area under line segment BC)- (area under line segment AC)
Let line AB, BC and AC be l, m and n respectively.
Equation of l, by two-point form, will be or y=2x-1.
Equation of m, by two-point form, will be or y=8-x.
Equation of n, by two-point form, will be or .
Hence, the area of triangle whose vertices are (2,3), (3,5) and (4,4) is square units.
Rate this question :