15. Let r be a positive real number. The equation for a circle of radius r whose center is the origin is x² + y² = r². dy dx (a) Use implicit differentiation to determine (b) Let (a, b) be a point on the circle with a ‡ 0 and b ‡ 0. Determine the slope of the line tangent to the circle at the point (a, b). (c) Prove that the radius of the circle to the point (a, b) is perpendicular to the line tangent to the circle at the point (a, b). Hint: Two lines (neither of which is horizontal) are perpendicular if and only if the products of their slopes is equal to −1.

Q: Find the points on the curve c where the tangent is vertical C: x= t - 48t, y = t + 12t. ОА (-128,…

A:

Q: Find the equation of the tangent line to the curve (a lemniscate) 2 (x² + y²)² = 25 (x² - y²) at the…

A:

Q: Let r be a positive real number. The equation for a circle of radius r whose center is the origin is…

A: Given equation: x2+y2=r2                     . . . (1) (a) Differentiating (1) with respect to x,…

Q: The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to…

A:

Q: Find the y-intercept of the tangent line to the curve y =x at the point (2,8).

A: We have given, The curve y = x3 and the point (2, 8).

Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: Find the slope of the tangent line to the graph of the function at the point (1, 0). y 4 3 2 1 /1,0)…

A:

Q: at (1, 3). Find the slope of the tangent to the curve x° + 3xy + y° = The slope is

A:

Q: Find a function γ that describes the circle of radius 3 centered at z = 3 - 2i.

A: