Question

The curve y^2 = 12x intersects the line 3y = 4x + 6 at two points. Find the distance between the two points.?

Answer 1

Step 1 :

The curve is and the line is .

The curve intersects the line .

The line equation is .

Solve for y .

Divide each side by 3.

.

Substitute in .

If , then .

If , then .

Thus, the intersection points are and .

Step 2 :

Find the distance between the intersection points.

Let the points are and .

Distance between two points : .

The distance between the two intersection points :

The distance between the intersection points is units.

Solution :

The distance between the intersection points is units.