Question

a. Verify that the given point lies on the curve.

b. Determine an equation of the line tangent to the curve at the given point.

9 (x² y²)² =100xy² ; (1,3)

Answer 1

a) To verify the point (1,3) lies on above equation

For that we have to substitute the points in the equation and evaluate Left Hand Side and Right Hand Side

Since both Left Hand Side and Right Hand Side are equal , the point (1,3) lie on the given curve

b) The equation of tangent line is given by point - slope formula

where x1 , y1 are coordinates of any point on the curve

Here we already have a point on the curve (1,3)

Now we have to find the slope m = dy/dx

Equation of curve is given by ;

Taking derivative on both sides,

Evaluating Left hand Side,

EQUATION USED

• 

Applying Chain reaction rule,

  

  

  

  

Evaluating Right hand Side,

Applying product rule,

• 

  

  

Therefore

At point (1 , 3)