Question 1
At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (– 4, – 3). Find the equation of the curve given that it passes through ( 2, 1).
Solution
Let y = f(x) be equation of curve.
Now
is the slope of the tangent to the curve at the point (x, y)
From the given condition,
Separating the variables, we get,
Integrating,
...(1)
Since curve passe through (-2, 1)
which is required equation of curve.
Now
is the slope of the tangent to the curve at the point (x, y)From the given condition,
Separating the variables, we get,
Integrating,
...(1)Since curve passe through (-2, 1)
which is required equation of curve.
whose differential equation is 
is