(1 point) find a vector function that represents the curve of intersection of the paraboloid z=8x2+3y2z=8x2+3y2 and the cylinder y=5x2y=5x2. use the variable t for the parameter.

Answer-

The vector function that represents the curve of intersection of the given paraboloid and cylinder is,

Solution-

Here we have to calculate the vector function represents the curve of intersection of the paraboloid '' z = 8x²+3y² '' and the cylinder " y=5x² "

All are in rectangular form and we have to convert them into parametric form.

putting it in the equation of the cylinder equation we can get the value of y, so

Now, we have the values of x and y in parametric form. Putting the values of x and y in the paraboloid equation, we can get the value of z, so

∴ Vector function that represents the curve of intersection is,