(a) Here's a Calculus 1 optimization problem you probably solved before. Show that the shortest distance from the origin to the line bx +ay = ab (where a and b are positive constants) is dmin= ab √a² + b²²

Q: Find 2 parabolas that shares the same vertex and focus with the ellipse 9x² + 25y² = 225

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Q: There is a parabola which has a minimum where the two lines 3x+6y-1=0 and 2x+ y-2=0 intersect. The…

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Q: graph the parabola y=(x-5)2-2

A: Consider the given equation

Q: What is the vertex of the parabola (y - 1)2 = 16x?

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Q: The surface of a mountain is modeled by the equation h(x, y) = 7500 – 0.001x2 - 0.004y2. A mountain…

A: Given the surface of a mountain is modeled by the equation h(x,y)=7500−0.001x2−0.004y2

Q: Solve the problem. A homeowner wants to make an elliptical rug from a 30-foot by 10-foot rectangular…

A: To solve this problem, we can use the fact that an ellipse can be defined by its semi-major axis…

Q: Graph the parabola   y=(x-3)2  +4

A: Given, the parabola equationy=(x-3)2  +4The entire parabola translates 3 units to the right and 4…

Q: Graph the Ellipse and label the intercepts y = 5(x+3)²-3

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Q: write in standard(vertex) form the equation for the parabola which has the following properties:…

A: Given, Parabola equation has zeros at x=1 and x=7. Maximum value = 12 The standard form of the…

Q: Solve for the directrix of the parabola y2 + 8x = 32

A: We have to solve for the directrix of the parabola y2 + 8x = 32.

Q: Determine the ends of the minor axis of the following ellipse: .(x+3)² (y+4)² = 1 16 25 O (-7, -4)…

A: Use ellipse concept

Q: Find an equation of the parabola with vertex (2, −3) and focus (2, −7).

A: (a) The standard  equation of parabola  is           (x - h)2 = 4p (y - k), where the focus is (h, k…