JEE Advance - Mathematics (2004 - No. 8)
A curve $$'C''$$ passes through $$(2,0)$$ and the slope at $$(x,y|)$$ as $$\,{{{{\left( {x + 1} \right)}^2} + \left( {y - 3} \right)} \over {x + 3}}$$. Find the equation of the curve. Find the area bounded by curve and $$x$$-axis in fourth quadrant.
Area = 2/3 sq. units, Equation: y = (x+1)^2 + 3ln|x+3| - 1 - 3ln5
Area = 4/3 sq. units, Equation: y = (x+1)^2 + 3ln|x+3| - 1 - 3ln5
Area = 4/3 sq. units, Equation: y = (x+1)^2 - 3ln|x+3| - 1 + 3ln5
Area = 2/3 sq. units, Equation: y = (x+1)^2 - 3ln|x+3| - 1 + 3ln5
Area = 1 sq. units, Equation: y = (x+1)^2 + 3ln|x+3| - 1 - 3ln5