Verify that the given point lies on the curve. Determine an equation of the line

Question

Verify that the given point lies on the curve. Determine an equation of the line tangent to the curve at the given point. 5x2 + xy + 5y2 = 44; (22) How do you know that the point is on the given curve? The value of 5x2 + xy + 5y2 is less than 44 when x is 2 and y is 2. The value of 5x2 + xy + 5y2 is 44 when x is 2 and y is 2. The point (22) is in the first quadrant. The point (22) is in the domain of the implicit function. Write the equation for the tangent line in slope-intercept form. Y = (Use integers or fractions for any numbers in the equation.)

Explanation / Answer

a) to verify whether the point lies on the curve you have to just substitute the point back into the curve and check if it satisfies the equation. b) calculate y' and the tangent equation would be y-y1 = y'(x-x1) convert it into the for y = mx + c which is the solpw intercept form. m= slope of the tangent c= y intercept

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