IIT JEE Diameter Slope

TL;DR

The slope of the line joining two points on a parabola can be expressed as 2/r.

Transcript

Let A and B be two distinct points on the parabola y squared is equal to 4x. If the axis of the parabola touches a circle of radius r, having AB as its diameter, then the slope of the line joining A and B can be. So let's draw this. So let me draw my axes here. That's my y-axis. And here is my x-axis. And then the parabola y squared is equal to 4x ... Read More

Key Insights

• 🤗 The parabola y^2 = 4x is a symmetrical graph that opens to the right.
• 👈 The diameter of a circle touching the x-axis can be formed using two points on the parabola as its endpoints.
• 😥 The coordinates of the midpoint of the diameter can be found by averaging the coordinates of the two points.

Questions & Answers

Q: How is the parabola y^2 = 4x represented on a graph?

The parabola y^2 = 4x is symmetric and opens to the right. It can be divided into two parts: y = 2√x and y = -2√x.

Q: What is the relationship between point A, point B, and the radius of the circle?

The sum of the x-coordinates of points A and B is equal to the radius of the circle.

Q: How can the coordinates of the midpoint of AB be calculated?

The coordinates of the midpoint are found by taking the average of the x-coordinates and the average of the y-coordinates of points A and B.

Q: What is the slope of the line joining points A and B?

The slope of the line is equal to 2/r, where r is the radius of the circle.

Summary & Key Takeaways

• The parabola y^2 = 4x is graphed and points A and B are chosen on the parabola.

• The diameter of a circle, with AB as its diameter and touching the x-axis, is constructed.

• The coordinates of the midpoint of AB are found, which is equal to r, the radius of the circle.

• The slope of the line joining points A and B is determined to be 2/r.