Question

Use a graphing utility to sketch the intersecting graphs of the equations and show that they are orthogonal. [ Two graphs are orthogonal if at their point(s) of intersection their tangent lines are perpendicular to each other.]

2x^2 + y^2 = 6

y^2 = 4x

Answer 1

Step 1:

The functions are  and 

Find intersection points.

Substitute in .

At  ,

At  ,

The intersection points are

Answer 2

Step 2:

The functions is .

Differentiate with respect to .

Use the power rule of derivative :

Use the constant rule of derivative :

The slope .

At point slope is .

The slope point form is .

Substitute in .

At point the tangent line is

Answer 3

Step 3:

The slope .

At point slope is .

The slope point form is .

Substitute in .

At point the tangent line is

Answer 4

Step 4:

The functions is

Differentiate with respect to .

Use the power rule of derivative :

The slope .

At point slope is .

The slope point form is .

Substitute in .

At point the tangent line is

Answer 5

Step 5:

The slope .

At point slope is .

The slope point form is .

Substitute in .

At point the tangent line is

Step 6:

Graph:

Observe from the graph :

Both the tangents are orthogonal to each other.

Solution: