Geometrical Applications Problem No 2

TL;DR

Given the slope of the tangent and the angle made by it, find the equation of the curve.

Transcript

click the Bell icon to get latest videos from equator hello friends in this video we are going to see one more problem which is based on geometrical application of differential equation let us start with problem number 2 y is equal to f of X crosses the x axis making an angle of 135 degree and the slope of the tangent at any point is 2x minus 3 fin... Read More

Key Insights

• ⚾ The problem involves finding the equation of a curve based on the slope of the tangent and the angle made by it.
• 🆘 Equating the slope equation to the tangent of the given angle helps find the value of X.
• ☺️ Substituting the value of X into the general equation of the curve and solving for the constant C gives the specific equation of the curve.
• ❣️ Intersection with the x-axis implies that the value of y is equal to zero.
• 🥺 Integrating the slope equation leads to the general equation of the curve.

Questions & Answers

Q: What information is given in the problem?

The problem provides the angle made by the tangent (135 degrees) and the slope of the tangent (2x - 3).

Q: How is the value of X determined?

By equating the slope equation (2x - 3) to the tangent of the given angle (tan 135 degrees = -1), the value of X is found to be 1.

Q: What does it mean for the curve to intersect the x-axis?

When the curve intersects the x-axis, the value of y will be equal to zero.

Q: How is the equation of the curve obtained?

By integrating the slope equation (dy/dx = 2x - 3), the general equation of the curve is found to be y = x^2 - 3x + C. Substituting the known values (X = 1, Y = 0), the value of the constant C is determined to be 2.

Summary & Key Takeaways

• The problem involves finding the equation of a curve given the slope of the tangent and the angle made by it.

• By equating the slope equation to the given angle's tangent, the value of X can be found.

• Substituting the value of X into the general equation of the curve and solving for the constant C gives the specific equation of the curve.